Multi-Stage Multi-Bet Game, Gaming Device, and Method

ABSTRACT

A game is comprised of a plurality of stages. Each operation of the game begins with the operation of a first stage. Depending on the outcome of the first stage the game may be over, or there may be an operation of a second stage. Depending on the outcome of the second stage, the game may be over or there may be an operation of another stage. This sequence continues until the game ends or until the final (n th ) stage has been operated, at which time the game ends. Wagers are made on successive stages of the multi-stage game. Each stage of the game may typically have its own paytable or payout scheme, and its own expected return.

This application is a continuation of application Ser. No. 13/211,235,filed Aug. 16, 2011, which is a continuation of application Ser. No.12/875,037, filed Sep. 2, 2010, which is a continuation of applicationSer. No. 11/182,407, filed Jul. 15, 2005, which is a divisionalapplication of application Ser. No. 10/435,650, filed May 9, 2003, whichis a divisional application of application Ser. No. 09/709,922, filedNov. 10, 2000. The entire contents of application Ser. No. 12/875,037are incorporated by reference.

FIELD OF THE INVENTION

This invention relates to games in general, and particularly to gamingmachines allowing wagers to be placed on a game, and more particularlyto an innovative casino-type gaming machine which allows wagers on aplurality of game levels.

DISCUSSION OF THE PRIOR ART

There are many ways in which multiple wagers may be placed on differentgaming machines. In one of the simplest forms, a player may make avariable wager on a specific bet. On a single line slot machine forexample, as the player inputs additional coins into the machine (perplay) the payouts for the single payline is multiplied by the number ofcoins bet. Often the higher awards increase beyond the given multiple,offering a bonus for betting more coins on this single payline. The sametype of multiple coin bet is also well known in video poker, where atypical bet is one to five coins on each hand played. In such a videopoker game, the paytable is multiplied by the number of coins bet with asubstantial bonus being given for a Royal Flush when five coins are bet.

In other gaming machines, there are multiple bets that can be made ondifferent outcomes. In a multiline slot machine for example, a wager canbe made on each of a plurality of paylines. Typically, each payline ispaid according to a paytable (also referred to as a “payout table”) thatis similar for each payline. A single spin of the reels yields a resulton each payline which is paid if it matches a winning combination on thepaytable.

The above two techniques have been combined, providing multiple paylinesand multiple coins per payline. The pay for each payline is multipliedby the number of coins bet on that payline with certain bonusesavailable when a higher number of coins per payline are wagered.

Additionally, there have been games such as Double-Down Stud poker whichallow a player to place an additional bet on a game that is already inprogress. There have been games such as Play-It-Again poker which allowa player to make a new bet on a re-play of a starting hand.

Thus, it can be appreciated that there have been poker games, forinstance, which allow a player to bet on multiple hands where each ofthe plurality of hands is generated from a single initial deal, followedby independent draws or re-deals for each hand that received a bet. Ineach case, the bets that are made are considered to be made on a game ofchance, and paid if there is a winning result.

SUMMARY OF THE INVENTION

In broad overview, the present invention in one aspect allows theplacing of multiple bets on different stages of a game. The game iscomprised of a plurality of stages. Each operation of the game beginswith the operation of a first stage. Depending on the outcome of thefirst stage the game may be over, or there may be an operation of asecond stage. The second stage operation may be totally independent ofthe first stage, or may have dependencies on first stage events or data,e.g., the achievement of a “winning” first stage. As will be understoodthroughout this invention disclosure, “winning” is just one form ofpossible advancement to the next level. For example, one aspect of theinvention includes a “special card” (Free Ride) which permitsadvancement even if a “losing” condition is presented at a level.

Depending on the outcome of the second stage, the game may be over orthere may be an operation of a third stage. This sequence continuesuntil the game ends or until the final (n^(th)) stage has been operated,at which time the game ends.

It should be appreciated that not every stage will operate in each game,and that the lowest stages will operate the most often while the higheststages will operate the least often.

As noted above, the present invention furthermore allows the player toplace wagers on different stages of the multi-stage game. Each stage ofthe game may typically have its own paytable or payout scheme, and itsown expected return. A bet made on a stage of the game which is notplayed is lost in one contemplated form of the invention. Thus, at thehighest stages the bets made are lost very often, without even playingthat stage of the game, because most games will end before getting tothe highest stage bet. Due to this architecture, there is much greateropportunity for large wins in games which get to the highest stages.This makes for a more exciting gaming experience, because as the playerswatch the game successfully continue through the various stages, theexpectation of what may be won at each stage usually increases.

Embodiments shown herein are generally constructed such that the playerspecifies at the outset of the game the number of stages or levels tobet on. For instance, bets are made on a first level, a second level,and up to the number of levels specified by the player. While this isone preferred embodiment which gives the player action at all levels upto the highest level bet, it is envisioned that the player could beallowed to arbitrarily choose which levels to bet without departing fromthe invention. So too, it is contemplated that the game could allow fora new bet as stages are achieved.

Certain contemplated embodiments also have a structure that any “Win” ona given stage advances the game to the next stage. Other contemplatedembodiments have different game rules for continuing from stage tostage, and operate under those rules for a given stage.

In one aspect of the invention, it is a principal objective to provide amethod of playing a game, where a player is initially provided with afirst stage game of chance upon which a first wager is placed by theplayer, and a second stage game of chance upon which a second wager isplaceable. As previously noted, the game stages can be the same type ofgame (e.g., slots), or different games (e.g., slots, cards, dice,roulette, etc.).

Each stage has a “winning” condition and a “losing” condition. That is,there is an established criterion or criteria whereby the player mayadvance from one stage to the next, or may not. As used throughout thisdisclosure, and in the claims, “winning” and “losing” are to beconsidered synonymous with advancing or terminating, unless otherwisestated.

The first stage game is played, with a determination of whether awinning/advancement or losing/terminating condition is presented. If awinning condition is presented by the first stage game as played, thenthe player advances to the second stage game, assuming a bet has beenpreviously placed for that stage. If a losing condition is presented bythe first stage game as played, however, the game is over and any secondwager (or higher) is lost. It will be understood that in someembodiments a loss condition could be presented by simply achieving acondition where only part of a wager placed on a given level may bereturned, i.e., a player wagered 5 on a level but only achieved a returnof 3. So too, all of the bet need not be lost as a terminating/losingcondition.

In the event that the first stage presents a winning condition and thereis a wager for the second stage, then the second stage game is played.There follows a determination as to which of the winning and losingconditions is presented by the second stage game as played. These stepsare repeated for as many stages as are provided by the game if all havebeen bet upon, or as many stages as have actually been bet upon if fewerthan all, again assuming a winning/advancement condition has been metfor each preceding stage.

In a preferred form the foregoing method of playing a game includes thestep of providing a payout for a winning condition at the second stage,or more preferably providing a payout for a winning condition at eachstage. The payout can be based upon the amount of a respective wager ata respective stage, and advantageously includes an increase by amultiplier for a payout at a respective stage, with the multiplierincreasing for each successive stage.

In another aspect of the invention, the foregoing method is adapted foroperating a processor-controlled gaming machine. In this application ofthe invention, gameplay elements are provided in a manner that can bevisualized by a player, such as on a video display screen, or in somethree dimensional format where the gameplay elements can be tracked(such as on a board with an electronic interface), just to name two waysof such visualization. In this form of the invention, a mechanism for awager input from the player is also provided, along with a mechanism forgame operational input from the player, such as to start play.

There is a first stage game of chance upon which a first wager is placedby the player, and at least a second stage game of chance upon which asecond wager is placeable. Each stage has a winning/advancementcondition and a losing/terminating condition. In the preferred form ofthe invention, all wagers are placed before play begins at the firststage level.

This gaming machine displays at least the first stage game using atleast some of the gameplay elements. For instance, using a video monitoras an example, a first slot machine may be displayed (or first displayof cards, or dice, etc.). More than one stage may be displayed at a time(e.g., a plurality of slot machine representations stacked one on top ofanother on the display). The first stage game is then played, with thepreviously described determination of which of the winning and losingconditions is presented by the first stage game as played. Again, if awinning condition is presented, the player advances to the second stagegame, but if a losing condition is presented by the first stage game asplayed, the game is over and at least some (and most preferably all) ofthe second (and any subsequent) wager is lost.

If not already displayed, and assuming there has been an advancingcondition met at the first stage and a bet placed on the second stage,the second stage game of chance is displayed (or, for instance,activated if already displayed). This second stage is played, with adetermination of which of the winning and losing conditions is presentedby the second stage game as played. If there is a winning condition,this form of the invention provides a payout for the second stage, aswell as for any subsequent consecutive stage for which there is awinning condition, and a wager placed thereon.

One embodiment of this method as applied to a gaming machine provides aset of differing gameplay element indicia, such as facets of a die. Asubset of at least one match indicia against which a set of dice are tobe matched in the course of play is established, such as a randomselection of die faces (e.g., three die numbers against which tosseddice are to be matched. In a preferred form of this dice gaming machine,first, second, third and successive stages up to said nth stages aredisplayed together as discrete arrays on a visual display.

The dice are initially tossed in one embodiment, and beginning with atleast the second stage game, a determination is made as to whether anymatch is made between the match indicia and the dice tossed. At leastone match comprises a winning condition for a stage being played, inthis embodiment. If a match is not made, then the unmatched indicium isremoved from further play. The game ends when no matches are made at agiven level, again assuming that a wager has been made up to andincluding that level.

Yet another aspect of the invention is providing a feature which issubject to random allocation to a stage in the course of play, with thefeature if allocated enabling a next stage to be played regardless ofwhether a winning condition has otherwise been presented. The feature,referred to herein as a “Free Ride,” therefore constitutes or comprisesa so-called winning/advancement condition. Of course, a wager stillneeds to have been placed on the next stage which is subject to being soenabled for play by the Free Ride feature.

A video card game comprises yet another form of the invention. Here, avideo display device is driven by a cpu having a program. A wager inputmechanism registers a wager placed by a player, with the wager includingan ability to register bets upon successive stages of the game. A firstdeck of playing cards comprised of cards of suit and rank is generatedby the program, with the program establishing a first array for displayof a subset of the deck (i.e., a hand) of cards randomly selected fromthe deck.

A first stage hand of cards is dealt. The card game could be one inwhich the hand as so dealt is not subject to a draw, or the player canselect cards to discard, with a new card taking the place of anydiscarded. In either event, the hand ultimately becomes set, and adetermination is made as to whether the hand of cards presents awinning/advancement condition based upon a preset hierarchical rankingof card arrangements relating to suit and rank. As in the situationsnoted above, subsequent hands of cards are dealt if a winning conditionis presented by the previous hand, provided a bet has been registeredfor each successive stage. If a losing condition is presented by astage, or a stage is reached upon which no wager has been made, the gameis over. Bets on any higher stage are lost if a losing condition ispresented, as is the bet on the stage for which the losing condition isregistered. A payout output based upon the wager and predeterminedvalues for a stage is preferably provided according to a presethierarchical ranking of card arrangements relating to suit and rank. Thepayout output can include payout tables which are different for at leastsome of the stages, and may further include a multiplier for at leastsome of the stages, with the multiplier increasing for successivelyhigher stages.

In a video slot machine version of the invention, a plurality ofrotatable reels is generated by the computer program, each of the reelsbeing comprised of a plurality of different indicia. Each of the reelsis caused by the program to appear to rotate and then randomly stop tothereby yield a display of certain indicia as a spin. If an advancementcondition is presented on the first stage spin, a second stage spinoccurs if a bet has been registered for that second stage spin, and soforth. The first stage spin can be visually displayed as a first set ofreels in a first array, with the second stage spin likewise visuallydisplayed as a second set of reels in a second array, and successivestage spins each so displayed as further sets of reels in successiverespective arrays, with a plurality of arrays being displayed togetheron the visual display. Alternatively, one set of reels could berepeatedly spun for each stage. Payouts and multipliers can be providedin like manner to that described above for the card game embodiment, oras otherwise may be desired. One variant of the slot machine version ofthe invention has the multiplier for the games nth stage spin (the lastpossible level) randomly selected by the program from a predeterminedtable of multipliers, where at least most of the multipliers are greaterthan a multiplier for any previous stage. This random multiplier canadvantageously be displayed, or physically embodied, as a wheel havingsegments with the multipliers displayed in respective segments of thewheel. The wheel is caused to rotate and come to a stop with the randommultiplier at a designated stop point.

Of course, the foregoing invention as described in a video slot machineembodiment could be readily embodied in a standard mechanical slotmachine. Likewise, the video dice game is readily adapted to atable-type game format, as is the video card game contemplated above.

In the same vein, a gaming machine coming within the scope of one aspectof the invention broadly comprises a gaming unit having at least firstand second stages of play, each stage having an advancement conditionand a non-advancement condition. Some kind of interface mechanism withthe gaming unit allows gameplay input for a player, with the gameplayinput including wagering input allowing the player to register a betupon one or more stages of play.

An operational device operates the gaming unit, upon player inputincluding an operational command. The operational device determineswhich of the conditions is presented by a first stage as played, and ifan advancement condition is presented, then advancing the gaming unit tothe second stage, but if a non-advancement condition is presented, thegame is over and at least a portion, and preferably all, of any secondstage bet registered is lost. Play continues for a successive stage upto a predetermined nth stage if an advancement condition is determinedfor that next stage to be reached, and a bet has been previouslyregistered for that successive stage. Again, the stages of play can begames which are of the same type of game, or different types of games.These can also be games that have not yet been invented.

These aspects of the invention, along with other aspects, advantages,objectives and accomplishments of the invention, will be furtherunderstood and appreciated upon consideration of the following detaileddescription of certain present embodiments of the invention, taken inconjunction with the accompanying drawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a video screen representation highlighting three paylines of astage of a video slot machine embodiment of the present invention;

FIG. 2 is a video screen representation similar to FIG. 1 highlightingfive paylines;

FIG. 3 is a video screen representation of a three stage slot machineembodiment of the present invention;

FIG. 4 is a representation of a paytable of winning combinations for theslot machine presented in FIG. 3;

FIG. 5 is a representation of a continuation of the paytable of FIG. 4;

FIG. 6 is another video screen representation of the slot machineembodiment of FIG. 3 of the present invention;

FIG. 7 is another video screen representation of the slot machineembodiment of FIG. 3;

FIG. 8 is another video screen representation of the slot machineembodiment of FIG. 3;

FIG. 9 is another video screen representation of the slot machineembodiment of FIG. 3;

FIGS. 10 a-10 e present a flow chart of a method of operating a threestage video slot machine gaming machine of the type of embodiment ofFIG. 3;

FIG. 11 is a representation highlighting a bonus multiplier wheel foruse in a video slot machine embodiment of the present invention;

FIGS. 12 a-12 c present flow charts of a method of operating a videoslot machine gaming machine embodiment of the present invention usingthe bonus multiplier wheel of FIG. 11;

FIG. 13 is a video screen representation highlighting a multi-stagepoker gaming machine embodiment of the present invention;

FIG. 14 is a video screen representation highlighting a first stageresult on the poker machine embodiment of FIG. 13;

FIG. 15 is a video screen representation highlighting a second stage ofthe poker machine embodiment shown in FIG. 13;

FIG. 16 is a video screen representation highlighting a third stage ofthe poker machine embodiment of FIG. 13;

FIG. 17 is a video screen representation highlighting anothermulti-stage poker gaming machine embodiment of the present invention;

FIG. 18 is a representation of a paytable of winning combinations of thepoker gaming machine embodiment of FIG. 17;

FIG. 19 is another video screen representation of the poker gamingmachine embodiment of FIG. 17;

FIG. 20 is another video screen representation of the poker gamingmachine embodiment of FIG. 17;

FIG. 21 is another video screen representation of the poker gamingmachine embodiment of FIG. 17;

FIG. 22 is another video screen representation of the poker gamingmachine embodiment of FIG. 17;

FIG. 23 is another video screen representation of the poker gamingmachine embodiment of FIG. 17;

FIG. 24 is a video screen representation of the poker gaming machineembodiment of FIG. 17, but with a different opening hand shown using a“Free Ride” card;

FIG. 25 is another video screen representation of the poker gamingmachine embodiment of FIG. 24;

FIG. 26 is another video screen representation of the poker gamingmachine embodiment of FIG. 24;

FIGS. 27 a-27 f present a flow chart of a method of operating a drawpoker video gaming machine of the present invention;

FIG. 28 is a video screen representation of a multi-stage video dicegaming machine embodiment of the present invention;

FIG. 29 is a video screen representation highlighting a first stage orroll of the dice of the dice gaming machine embodiment of FIG. 28;

FIG. 30 is a video screen representation of a second stage of the playof the dice gaming machine embodiments of FIG. 28;

FIG. 31 is a video screen representation of a third stage of the play ofthe dice gaming machine embodiment of FIG. 28;

FIG. 32 is a video screen representation of a fourth stage of the playof the dice gaming machine embodiment of FIG. 28;

FIG. 33 is another video screen representation of the dice gamingmachine embodiment of FIG. 28; and

FIGS. 34 a-34 d present flow charts for a method of operating a videodice gaming machine of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

Four different embodiments of the present invention are describedherein, with some noted variations in certain cases. The firstembodiment is a three stage, multi-line, multi-coin video slot machine.The same game format (slots) with the same paytable is operated on threestages, with increasing payout multipliers at each stage providing anincreasing amount to win at the higher stages. The “spin” at each stageis independent of the previous stages.

The second embodiment is a multi-stage Five-Card Stud poker game. Eachstage is again independent of the previous stage. However, a separatepaytable is used for each stage in this embodiment. A variation of thisgame is also shown which uses the same paytable on each stage, butcombined with a mechanism to increase the “hit” rate.

The third embodiment is a Draw poker game that combines the conceptsshown in the Stud poker game with the decisions and optimal playanalysis that are integral to Draw poker. The final embodiment is a dicegame which has been adapted to provide a high dependency between thefirst stage and the next stages.

While each of these embodiments uses a single game format, or type, toplay from stage to stage, as noted above, it is clearly anticipated thatthe invention may be used with a first game type as a first stage, witha subsequent stage or stages being of a different game type, e.g., asingle line slot stage, then a multi-line slot stage, then a Stud pokerstage, etc. Thus, it should be appreciated that similar or differentgames of chance may be staged together, and the invention is not limitedto the types of games shown here, and would encompass any conceivableother game, such as roulette, craps, baccarat, keno, and so on. It willalso be apparent to one of skill in the art how to use the invention inlive games with dealers (i.e., table games), notwithstanding theparticular embodiments described herein relating to gaming machines.

Triple-Strike Slots

A first embodiment of this invention takes the form of a multi-stageslot machine. This may be done on a video screen with the presentationof a video slot machine, or may be accomplished with mechanical spinningreels, for instance. In a mechanical embodiment, the stages may beplayed sequentially on the same reels, or on physically separate reels.It is also adaptable for combinations of video slots and mechanicalspinning reel slots, where some stages are played on the video slots andsome stages are played on mechanical spinning reels.

In this first embodiment, there are three video slot machines (stages)vertically disposed on a video screen (although it will be apparent howto adapt this technique to any number of desired stages). In thisembodiment, each machine has the same symbols, symbol frequency, hitrate and payout percentage. Of course, other embodiments may usedifferent hit rates and frequencies, if not entirely different symbolsand game themes from stage to stage.

In this first embodiment, the criterion for advancing from one stage tothe next is any win on the current stage. It is envisioned that othercriteria may be used in other embodiments, such as a special symbol,which while only paying in certain configurations, would advance aplayer to the next level anytime it appeared in the game.

Turning now to FIG. 1, the first embodiment has each stage as afive-reel, five-line video slot machine. This is of a type of slotmachine often called “Australian style.” This machine allows the playerto make a wager on one to five paylines, and allows a bet from one tonine coins bet on each payline for a maximum of forty-five coins bet pergame. FIG. 1 shows the first three paylines, with payline 1 drawnhorizontally across the center symbols, payline two drawn across theupper symbols and payline three drawn across the lower symbols.

FIG. 2 is the same as FIG. 1, with fourth and fifth paylines added. Thefourth payline is in the shape of the letter “V” while the fifth paylineis an inverted “V”. It is well known by those skilled in the art how todesign such a machine with more or fewer paylines, and more or fewercoins per line. It is also well known in the art, and envisioned forthis type of game, to include special bonuses or bonus rounds forcertain symbol combinations. Certain combinations have been included forthis purpose in the present description, but the special bonuses andbonus rounds have been replaced by fixed awards for clarity ofpresentation.

FIG. 3 shows a screen with three stages displayed. For each game played,the player selects from one to fifteen paylines (i.e., five paylinestimes three stages) to play or “activate”. The player operates themachine by pressing (actuating) buttons through the use of a touchscreendisplay, some pointing device, or through the use of correspondingmechanical pushbutton switches. The player may repeatedly press the“Select Lines” button 12 in FIG. 3 to select one to fifteen lines. Onemay also press the “Select 5 Lines”, “Select 10 Lines” or “Select 15Lines” buttons (14, 15 and 16, respectively) to select all lines of thefirst, first and second or all three machines respectively. As usedherein, “machine” refers to each separate slot display 18, 19, 20 (whichwill variously be referred to as machine, stage and level). Selectingfrom one to five lines will activate the lines on the lower machine 18and allow a “spin” (play) on the lower machine 18. Selecting from six toten lines will activate the five lines on the lower machine and one tofive lines on the second machine 19. This will then allow a spin on thefirst machine 18; if there is any winner on the first machine 18, a spinon the second machine will then follow. All amounts won on the secondmachine 19 are multiplied by two (2×) in this version (see window 22).

Selecting from eleven to fifteen lines will activate the five lines onthe first machine 18, the five lines on the second machine 19 and fromone to five lines on the third machine 20. This will then allow a spinon the first machine 18, and if there is a winner on the first machine,then a spin on the second machine 19 (with 2× payout following). Ifthere is any winner on the second machine 19, that will allow a spin onthe third machine 20. All amounts won on the third machine 20 aremultiplied by four (4×) in this version (see window 23).

In this particular embodiment, the “hit rate” (percentage of games thathave any win) is carefully set just over 50%. This allows each stage(18, 19 and 20) to have a multiplier that is twice that of the previousstage, and result in a reasonable expected payout for the player andreasonable expected return for the operator (e.g., gamingestablishment). More stages could be added in a manner described withoutdeparting from the invention. Also, vastly different hit rates andmultipliers could be used, separate paytables for each stage that do notscale evenly may be used, and other variations thereon will be readilyapparent to those of skill in this art.

It should be noted that bets on the second machine 19 (lines six throughten) and the third machine 20 (lines eleven through fifteen) will belost if a machine at a stage (level) below it does not result in a win,in this embodiment. This is considered offset in the mind of the playerby game multipliers (2× and 4× respectively) when these machines do geta chance to spin. This increased opportunity for winnings when theseupper stage machines get to spin adds a great deal of excitement andanticipation for the player.

Once the player has selected the number of lines, he or she specifieshow many coins are to be wagered for each of the selected lines. As iswell known in the art, all payouts are multiplied by the number of coinsbet per payline. The player may repeatedly press the “Coins Per Line”button 25 (FIG. 3) to select one to nine coins-per-line. The total betis the product of the number of lines selected (button 12) and thenumber of coins-per-line, and is shown in the “Total Bet” meter 26.

FIG. 4 and FIG. 5 show the paytables indicating the available winningcombinations and rules governing those combinations. These paytables maybe displayed at any time by pressing the “Pays” button 28 (shown, e.g.,in FIG. 3). The “Help” button 29 may be pressed at any time for anoverall description of the rules of the game and its operation. Again,these buttons, their operation and related programming, are well known.

Once the specifics of the bet are selected as described above, theplayer presses the “Spin Reels” button 30, which will initially spin thereels on the first slot machine 18. If there is no winning combinationon any active (bet) payline then the game is over and the entire bet islost, including any amount bet on the other machines 19, 20. If there isany winning combination on an active payline of the first machine 18,then the machine display will first show all winning paylines followedby a pattern of cycling through the individual winning combinations.

FIGS. 6 and 7 show how the game cycles through multiple winningcombinations of the first machine 18. In FIG. 6, the single “WILD”symbol is shown as a winner on payline 1. The machine draws boxes, forinstance, around the winning symbols on the payline. In the payoutinformation window 21 to the right of the first machine 18, the top linecalls out “Line 1: 2 Coins”. This indicates the two coins awarded forone “WILD” symbol on payline 1, as confirmed by the paytable in FIG. 4.After showing the display of FIG. 6 for a few seconds, the machine showsthe display of FIG. 7, which calls out the next winning combination.FIG. 7 shows three cow symbols on payline 5 (in boxes). The top line ofthe payout information window 21 now calls out “Line 5:5 Coins” inrecognition of the five coins won for the three cows on the fifthpayline (confirmed by the paytable in FIG. 5).

For both FIG. 6 and FIG. 7, the second line of the payout informationwindow 21 shows the total number of coins from all pays of the firstmachine (in this case “SubTotal: 7” consisting of the two coins from thefirst payline and the five coins from the fifth payline). The lower halfof the payout information window 21 then shows the total pay of themachine, times the machine multiplier, which for the first machine isone (1×).

This results in a “Total” of seven coins for the lower machine. The“Total Won” meter 36 on the right edge of the screen shows this sevencoin figure in FIG. 7. FIG. 6 and FIG. 7 show the second machine 19 “litup” and ready to spin as a result of the win on the first machine 18.

As a result of winning on machine 18, the player is now allowed to spinthe reels of the second machine 19, provided that a bet was placed on atleast one of lines six through ten. The reels on the second machine 19are spun by again pressing the “Spin Reels” button 30. If there is nowinning combination on the reels of the second machine 19, then the gameis over. In that case, any bet made on the third machine 20 (lineseleven through fifteen) is lost, and the winnings from the first machine18 are paid to the player. The game pays the awarded credits from firstmachine 18 then restarts, becoming ready to take another bet.

In the case of a winning combination on the second machine 19, then itmay have an overall display similar to FIG. 8. With only a singlewinning combination on the second machine, the machine boxes the “7's”symbol on its first payline, and shows in the second stage, payoutinformation window 22 that one coin was won for a “SubTotal” of one coinon the second machine 19. Since all pays on the second machine aremultiplied by two in this version (multiplier 2×), this results in atotal pay of two coins on the second machine 19. The “Total Won” meter36 is now updated to nine coins, which comprises the seven coins wonfrom the first machine 18, plus the two coins won from the secondmachine. Since the player bet five coins on the second machine 19 (oneeach on lines six through ten), this second machine result is actually anet loss of three coins. However, because it was not a total loser (zerocoins won), the player is now entitled to spin the third machine 20 if abet was placed on any of lines eleven through fifteen. FIG. 8 shows thethird machine 20 lit up and ready to spin as a result of the two coinwin on the second machine.

Once again, the reels on the third machine are spun by pressing the“Spin Reels” button 30. If there is no winning combination on the reelsof the third machine 20, then the game is over. In that case, thewinnings from the two other machines are paid to the player, and thegame recycles for a new bet.

A winning combination is shown on the third machine 20 in FIG. 9. Withonly a single winning combination on the third machine 20, the machineboxes the three “7's” symbols on its first payline, and shows in thethird stage payout information window 23 that twenty-five coins werewon, for a “SubTotal” of twenty-five coins on the third machine 20.Since all “pays” on the third machine are multiplied by four (multiplier4× for this version), this results in a total pay of one hundred coinson the third machine 20. The “Total Won” meter 36 is now updated to 109coins, to include the 100 coins won from the third machine. With thethird and final machine having been played, the total winnings of 109coins are now added to the total credits meter 37, and the game is readyto restart and receive another bet.

The “Max Bet Spin” button 39 (shown in FIGS. 3 through 9) provides a onetouch solution which will cause all fifteen lines to be selected withnine coins bet per line and spin the reels on the first machine 18,assuming enough credits are available. It is the same as pressing the“Select Lines” button 12 until “15” is selected, then pressing the“Coins Per Line” button 25 until “9” is selected, then “Spin Reels”button 30.

The above-described embodiment of a gaming slot machine is operationallysummarized in the flow charts of FIGS. 10A-E. FIG. 10A generallydescribes the start-up of the Triple-Strike Slots game. First, anassessment of whether credit(s) are present is undertaken beginning atstep 150. If none is present, then a check is made as to whether theplayer has inserted the relevant coin, credit card, etc., for thenecessary credit(s) at step 151. If so, then at step 152 the credit(s)are registered and displayed at the “Total Credits” meter 37 (e.g., FIG.3). All available player buttons are then activated for initiation ofplay at 155.

At this stage, the player enters a set-up loop where the player maychoose to add more credits or proceed with play at step 156. If creditsare added, these are registered (on the meter display 37) at step 158,and the program loops back to step 156 (via 155).

The “Coins Per Line” button 25 can alternatively be engaged from step156, causing the coins-per-line setting to be modified (as indicated atmeter 40, FIG. 3), as well as updating the value of the “Total Bet”window 26, as indicated at step 159. Once again, the program loops backto step 156.

Back at step 156, the player then can choose the lines upon which to betthrough operation of general “Select Lines” button 12. This causes thegraphics program to highlight the lines being designated at step 160.Alternatively, the special “Select Lines” buttons 14 through 16 could beused out of step 156, also resulting in a registration of the line groupselected (at step 161), then an update of the graphics at step 160.

From step 160, the number of lines bet is registered on lines-bet meter41 (e.g., FIG. 3), and updated if the lines bet has been modified up ordown, as indicated at step 162. The “Total Bet” window 26 is alsoupdated in view of the lines being bet. The player is then returned tostep 156.

Once the player has input the parameters of the wager, then the “SpinReels” button 30 is engaged. It should be noted that the foregoingselection sequence as to coins and lines to bet need not follow theorder indicated.

The player has the option of skipping all of the line and coins-per-lineselections, through resort to the “Max Bet Spin” button 39. A subroutinewill then execute at step 165 to assess the total credits the player hasprovided, and determine the maximum number of coins per line and themaximum number of lines (per an embedded look-up table) which can beplayed for the credit quantity shown in total credits meter 37, up to afixed maximum for the game. The graphics are updated accordingly at step166 to show the lines being bet (as at step 160), with a similar updateof the coins-per-line meter 40, lines-bet meter 41 and “Total Bet” meter26, all as indicated at step 167.

From either the actuation of the “Spin Reels” button 30 or the “Max BetSpin” button 39, the selection buttons for player input are thendeactivated and the amount bet is subtracted at step 168, with theremaining credits updated on the “Total Credits” meter 37. The displaygraphics then shows the reels spinning at the first stage/level/machine18 (step 169). The reel stop positions are selected in a random manner(step 170), with the graphics displaying the final symbols coming intoview for each reel in sequence (steps 171 a through 171 e).

Turning now to FIG. 10B, the program then assesses whether there is anywinning combination presented by the reels in their stop positions,taken in view of the paytable (FIGS. 4 and 5) and the lines bet, asindicated at step 175. If there is no winner, the game goes to a “GameOver” sequence (step 176 a), described hereafter. If there is a winner,then the winning line(s) are graphically highlighted on the display(step 177), the amount won is totaled and shown in the “SubTotal” areaof the first stage payout information window 21 (step 178), and the“SubTotal” amount is increased by the applicable multiplier (step 179),which in this first embodiment is 1× for stage one. This total formachine one is displayed in payout information window 21. The “TotalWon” meter 36 is accordingly updated (step 180).

An assessment is then made as to whether the player has bet on any linesof the second stage/level/machine 19, as noted at step 182. If not, thenthe game goes to the “Game Over” sequence (step 176 b). If a stage-twobet has been registered, then the player “Spin Reels” button 30 isreactivated at step 183. Machine two 19 is graphically highlighted onthe display (e.g., see FIG. 6), which may include flashing the button 30or the like to alert the player to continue play (step 184).

While waiting for the player to spin the second stage (machine two 19),like all other points that the program waits for input, a check is madeat 187 to see if additional credits have been purchased by the player.If more credits are input, they are registered on the “Total Credits”meter 37 (step 188), and the player is looped back to step 187.Ultimately, the “Spin Reels” button 30 is actuated by the player at step187, and play on the second machine 19 commences.

The button 30 is then deactivated (step 189), the second machine reelsare graphically shown spinning (step 190), and the sequence of steps 170and 171 a through 171 e described with respect to the first machine 18is repeated, except now as related to the second machine 19, as shown insteps 191 and 192 a through 192 e.

As shown in FIG. 10C, steps 195 and 197 through 200 then repeat theprocess for the second machine described in steps 175 and 177 through180, respectively, with regard to the first machine. Note that step 199increases the “Sub-Total” by 2× in this version, and the payoutinformation window 22 is utilized.

If a bet has been registered for lines on the third machine 20 (step202), the “Spin Reels” button 30 is again activated (step 203), machine20 is graphically highlighted on the display (e.g., see FIG. 8), whichmay include flashing the button 30 or the like to alert the player tocontinue play (step 204), and the player is again given the option ofadding more credits, or alternatively simply advancing to play the thirdstage (step 207). If more credits are input, they are registered on the“Total Credits” meter 37 (step 208), and the player is looped back tostep 207. Ultimately, the “Spin Reels” button 30 is actuated by theplayer at step 207, and play on the third machine 20 commences.

The “Spin Reels” button is once more deactivated (step 209), and steps210, 211 and 212 a through 212 e repeat steps 169, 170 and 171 a through171 e, respectively, this time for the third machine 20.

As shown in FIG. 10D, steps 215 and 217 through 220 then repeat theprocess for the third machine 20 described in steps 175 and 177 through180, respectively, with regard to the first machine 18. Note that step219 increases the “Sub-Total” by 4× in this version, and the payoutinformation window 23 is utilized (e.g., see FIG. 9).

FIG. 10E depicts the “Game Over” sequence out of either step 176 a or176 b. If out of step 176 a, the program “dims” the game display with a“GAME OVER” message (step 222). An assessment is made as to whetherthere are any credits in the “Total Won” meter 36 at step 223. If not,the player is returned to the start up sequence step 150 from step 224.

If there are credits won, then the “Total Won” credits are added to the“Total Credits” meter 37, accompanied by a bang, knocker or otherexciting sound, as indicated at step 225. If the “Game Over” sequence isengaged out of step 176 b, then the program cycles through step 225 then224, and returns to step 150.

Analysis of Certain Architecture of the Triple-Strike Slots Game

The multi-stage slot machine gaming machine embodiment being describedhas, as a base component, a single slot machine which is then adaptedfor a plurality of stages. The first step in the construction of thesingle machine of the game is to select the paying combinations for thestage, and then to lay out the symbols on the five reels in a manner toachieve the desired hit rate. The “hit rate” (percentage of games withat least one winning combination) in this embodiment is of importance,because getting a hit (or any win) is the criterion used to advance tothe subsequent stage. In this first embodiment, it was decided to usethe same machine at each stage with a doubling of the rewards for eachsuccessive level. If the “hit rate” for such a configuration was set atexactly 50%, then the expected return percentage would be the same foreach level. If the “hit rate” was less than 50%, then the player wouldget a lower expected return at each successive level, which is notdesirable in general. Moreover, certain gaming jurisdictions requirethat each additional coin bet on a game have the same or greaterexpected return than the previous coin.

If the “hit rate” is set at just over 50%, then each successive stagewill have a slightly greater return than the previous stage, which isdesirable to provide the player with an incentive to play more coins pergame. While it is easy to mathematically determine that the “hit rate”of any payline will be 18.64% in the described first embodiment, a morethorough analysis is needed to determine the “hit rate” when five linesare played. This is due to multiple winners on different lines oncertain spins. While the single line “hit rate” may be mathematicallydetermined using the quantities of each symbol on each reel, thefive-line “hit rate” requires knowledge of the actual layout of eachreel strip to take into account which pays will occur.

The first embodiment described above uses reel strips with thirty stoppositions laid out as shown in Table 1.

TABLE 1 Reel Stop # Reel 1 Reel 2 Reel 3 Reel 4 Reel 5 1 Scatter (Dice)Pumpkin Pumpkin Cow Dart Board 2 Dart Board Cow Pineapple Pineapple Cow3 Wild Wild Wild Wild Wild 4 Cow Dart Board Banana Dart Board Banana 5Banana Bonus (Drum) Cow Pumpkin Dart Board 6 7's Cow Pineapple ApplePineapple 7 Pumpkin 7's 7's Dart Board Bonus (Drum) 8 Apple Bonus (Drum)Apple Bonus (Drum) Apple 9 Scatter (Dice) Dart Board Banana Banana Cow10 Cow Banana Pineapple Pumpkin Banana 11 Banana Cow Cow Cow Pumpkin 12Bonus (Drum) 7's Apple Dart Board Cow 13 7's Dart Board Dart BoardPineapple 7's 14 Pineapple Pineapple Banana Pumpkin Scatter (Dice) 15Scatter (Dice) Bonus (Drum) Scatter (Dice) Bonus (Drum) Pineapple 16Apple 7's Pumpkin Banana Cow 17 Dart Board Cow 7's Dart Board 7's 18Bonus (Drum) Pumpkin Scatter (Dice) Apple Pumpkin 19 Banana Dart BoardPineapple Cow Dart Board 20 Pumpkin Apple Apple Banana Pineapple 21Scatter (Dice) Bonus (Drum) Bonus (Drum) Dart Board Bonus (Drum) 22Banana Pumpkin Banana Pineapple Banana 23 Cow Cow Apple Bonus (Drum)Dart Board 24 Bonus (Drum) 7's Bonus (Drum) 7's Pumpkin 25 PineappleDart Board Pineapple Dart Board Apple 26 Banana Pumpkin Banana PumpkinDart Board 27 Scatter (Dice) Bonus (Drum) Bonus (Drum) PineapplePineapple 28 7's Cow Apple Cow Scatter (Dice) 29 Cow Pineapple PineappleBanana Banana 30 Pineapple Dart Board Bonus (Drum) Pumpkin Pumpkin

With thirty stops on each of five reels, there are a total of 30⁵ or24,300,000 possible combinations. To determine the “hit rate” for thisset of reel strips, a computer analysis well known to the art is used toevaluate each of the 24,300,000 combinations of the five reels. For eachcombination, the symbols are analyzed across each of the five paylinesin comparison with the paytables and rules shown in FIG. 4 and FIG. 5.For each of the 24,300,000 combinations, if one or more of the paylineshas a winning combination or if a scatter pay is present, then a hitcounter is incremented. The analysis shows that for the reel strips ofTable 1 with the paytable information provided in FIG. 4 and FIG. 5,12,569,760 of the 24,300,000 combinations of the five reels result in awin, providing a 51.73% “hit rate.”

Table 2 shows the number of times each symbol appears on each of thefive reels. This frequency data is used in combination with Table 3 todetermine the payout percentage.

TABLE 2 Symbol Reel 1 Reel 2 Reel 3 Reel 4 Reel 5 WILD 1 1 1 1 1 7's 3 42 1 2 Apple 2 1 5 2 2 Banana 5 1 5 4 4 Pineapple 3 2 6 4 4 Pumpkin 2 4 25 4 Dart Board 2 6 1 6 5 Cow 4 6 2 4 4 Bonus (Drum) 3 5 4 3 2 Scatter(Dice) 5 0 2 0 2 30 30 30 30 30

Table 3 shows a table of the available “pays” along with the necessaryinformation to determine the payout percentage of the game. To providethe correct analysis, it should be clear that all “pays,” except the“Scatter” pay of three “Scattered Dice” symbols, will only pay left toright. That is, the indicated combination must be shown on successivereels starting with Reel 1 (see FIG. 1). The “WILD” symbol maysubstitute for any symbol except the “Bonus (Drum)” symbol and the“Scatter (Dice)” symbol. The “Scatter” pay will pay for three dicesymbols anywhere in the fifteen symbol visible display area. The“Scatter” pay will pay all paylines in addition to the highest pay oneach line. On each payline, only the highest combination is paid. Forthe purposes of the math table of Table 3, if there are two ways to makethe same highest pay value, then the combination using more symbols isused (e.g. “WILD-WILD-WILD-Banana-Any” is counted as four bananasinstead of three “WILDs”, both of which pay 50 coins).

The “Occurrences” column of Table 3 is created using the Table 2frequency data and enumerating each way to create that combination. Someexamples are shown for clarity:

5 “WILD” 1×1×1×1×1=1

One “Wild” symbol on each reel results in one Occurrence of five “WILD.”

4 “WILD” 1×1×1×1×(2+2)=4

One “WILD” symbol on each of the first four reels and either a Drum or aDice symbol on the fifth reel (any other symbol will result in five ofthat symbol instead of four wild).

3 “WILD” 1×1×1×3×30=90

One “WILD” symbol on each of the first three reels and a Drum on thefourth reel and any symbol on the fifth reel (any other symbol but aDrum on the fourth reel results in four or five of that symbol).

5 “7's” ((1+3)×(1+4)×(1+2)×(1+1)×(1+2))−1=359

Either a “WILD” or “7” on each reel, not counting the number of ways(one) to have five “WILDs.”

4 “7's” ((1+3)×(1+4)×(1+2)×(1+1)×(30−1−2))−(1×1×1×1×(30−1−2))=3213

The first component is the number of combinations with either a “WILD”or a “7” on each of the first four reels with any symbol except “WILD”or “7” on the fifth reel. This component includes combinations that havefour “WILDs” which either pay as four “WILDs” or five of some othersymbol, which need to be subtracted off. The second component is thenumber of combinations that have four “WILDs” on the first four reelsthat were part of the first component.

3 Bananas ((1+5)×(1+1)×(1+5)×(30−1−4)×30)−((1×1×1×(30−1−4)×30)=53250

The first component is the number of combinations with either a “WILD”or banana on each of the first three reels, with any symbol except a“WILD” or banana on the fourth reel and any symbol on the fifth reel.This component includes combinations that begin with three “WILDs,”which will pay as three “WILDs” or, four of some other symbol or five ofsome other symbol. The combinations with three “WILDs” are subtractedoff in the second component which includes the number of combinationsthat contain “WILD” on the first three reels, any symbol but “WILD” orBanana on the fourth reel, and any symbol on the fifth reel.

3 Scattered Dice (5×3)×30×(2×3)×30×(2×3)=486,000

Each of the five Dice on the first reel qualifies for the “Scatter” payin any of three positions (upper position, center position and lowerposition). This is multiplied by the thirty stops representing anyposition on the second reel, multiplied by the two Dice times threepositions on the third reel, multiplied by the thirty stops of thefourth reel, multiplied by the two Dice times three positions on thefifth reel.

All other counts in the “Occurrences” column are calculated in a similarmanner.

The “Probability” column for each row of Table 3 is computed by dividingthe “Occurrences” in that row by the total number of combinations whichis 24,300,000.

The EV or “Expected Value” for each row is computed by multiplying the“Pay” amount times the “Probability” for that row. The return from asingle stage of this machine is computed by taking the sum of all EVentries, which is 0.906239712, or a 90.62% return. The payout percentagecan be modified by modifying the Column 2 “Pay” values and thecorresponding paytable, as is well known in the art. The payoutpercentage may also be modified by changing the symbol frequencies shownin Table 2, and corresponding reel strips of Table 1. Care must be takento keep the “hit rate” at the desired level while changing the payoutpercentage. This is also well known in the art, and is often thepreferred method used to alter payout percentage, because when thismethod is used, the player cannot tell from the paytable which machinehas a higher return, or for that matter know for sure that machines areset at different payout percentages.

TABLE 3 Pay Symbols Pay Occurrences Probability EV 5 WILD 7500 14.11523E−08 0.000308642 4 WILD 200 4 1.64609E−07 3.29218E−05 3 WILD 5090  3.7037E−06 0.000185185 2 WILD 5 5,400 0.000222222 0.001111111 1 WILD2 529,200 0.021777778 0.043555556 5 7's 1000 359 1.47737E−05 0.0147736634 7's 100 3,213 0.000132222 0.013222222 3 7's 25 49,560 0.0020395060.050987654 2 7's 2 461,700 0.019 0.038 1 7's 1 2,025,000 0.0833333330.083333333 5 Apples 500 323 1.32922E−05 0.006646091 4 Apples 75 2,8890.000118889 0.008916667 3 Apples 15 28,350 0.001166667 0.0175 2 Apples 2108,000 0.004444444 0.008888889 5 Bananas 300 1,799 7.40329E−050.022209877 4 Bananas 50 8,975 0.000369342 0.018467078 3 Bananas 1053,250 0.002191358 0.02191358 2 Bananas 2 237,600 0.0097777780.019555556 5 Pineapples 250 2,099 8.63786E−05 0.02159465 4 Pineapples50 10,475 0.00043107 0.021553498 3 Pineapples 10 62,250 0.0025617280.025617284 2 Pineapples 2 227,700 0.00937037 0.018740741 5 Pumpkins 2001,349 5.55144E−05 0.011102881 4 Pumpkins 50 6,725 0.0002767490.013837449 3 Pumpkins 10 31,680 0.001303704 0.013037037 5 Dart Boards200 1,763 7.25514E−05 0.014510288 4 Dart Boards 50 7,032 0.0002893830.014469136 3 Dart Boards 10 28,290 0.001164198 0.011641975 5 Cows 2002,624 0.000107984 0.021596708 4 Cows 50 13,100 0.000539095 0.026954733 3Cows 5 78,000 0.003209877 0.016049383 5 Bonus (Drum) 1000 3601.48148E−05 0.014814815 4 Bonus (Drum) 150 5,040 0.000207407 0.0311111113 Bonus (Drum) 50 48,600 0.002 0.1 3 Scatter (Dice) 8 486,000 0.02 0.16Losing Spin 19,771,200 0.81362963 24,300,000 1 0.906239712

Building now upon the single stage machine so described, Table 4 showshow the return for the multi-stage version of the game is computed. Thefirst column shows the “Stage” for which the return is being computed.The second column shows the probability of a hit on the specified stage.In this first embodiment, this is the “hit rate” of a single stage ofthe machine, which is the criterion for moving up to the next stage. Thethird column shows the probability of playing the specified stage (asopposed to losing all bets on that stage without play). This is “1” forthe first stage (the first stage is always played), and for the otherstages is computed by multiplying the probability of playing theprevious stage (third column, one line above) times the probability of ahit on the previous stage (second column, one line above). For Stage 2,this is 1×0.51727=0.51727. For the third stage this is0.51727×0.51727=0.26757.

The fourth column shows the multiplier for all “pays” on the specifiedstage. This multiplier provides a reward that more than offsets thelosses for the times that the stage is not played. The fifth columnshows the EV for the machine on the specified stage, which is the samefor each identical machine in this embodiment. The sixth column showsthe overall EV of the specified stage, and is computed by multiplyingthe third through fifth columns together. This is because the EV of astage (fifth column) has to be scaled up by the payoff multiplier(fourth column) and reduced by taking into account the probability ofplaying that stage (third column). The seventh column shows thecumulative EV when one, two or three stages are played. This is theaverage of the sixth column of the specified level and all levels aboveit. When only one stage is played the cumulative EV is the same as theEV of that stage. When two stages are played, the cumulative EV is theaverage of the EV of the first stage and the second stage. When allthree stages are played, the cumulative EV is the average of the EV ofthe first stage, second stage and third stage. This results in anoverall expected return of 93.79% when all three stages (fifteen lines)are played.

TABLE 4 Multiplier Cumulative Probability Probability For Pays EV of Allof hit on this of Playing on this EV of EV of This Stages up to Stagestage This Stage Stage Machine Stage this Level 1 0.517274074 1 10.906239712 0.906239712 0.90624 2 0.517274074 0.517274074 2 0.9062397120.937548616 0.921894 3 0.517274074 0.267572468 4 0.906239712 0.9699391840.937909

A Variation on Triple-Strike Slots

In a modification to the first embodiment above, a fourth stage is addedallowing the player to wager on one to twenty lines. Instead of offeringa fixed 8× multiplier on the fourth stage, however, after any win on thefourth stage the multiplier is randomly selected from a range of 4× to50×, with weighted frequencies selected such that the overall value ofthe multiplier is about 8×. Each time that a spin on the fourth stageresults in any win, the game goes through a selection process thatpresents a multiplier of 4× to 50× to the player. One method ofpresentation is to select the multiplier and show it on the screen tothe player. Table 5 shows a table of weighted entries that are used forthis purpose. After a win on the fourth stage of this game, the machineuses its RNG (random number generator) to select an integer from 1 to29. This number is “looked up” in the second column of Table 5 (titled“Values”), and the corresponding value in the first column (titled“Multiplier”) is used as the stage multiplier for that spin. The thirdthrough fifth columns of Table 5 are used to determine the EV of thefourth stage multiplier in the same manner used in Table 3.

TABLE 5 Multiplier Values Occurrences Probability EV 50 1 1 0.034482761.724138 25 2 1 0.03448276 0.862069 10 3-5 3 0.10344828 1.034483 8 6-7 20.06896552 0.551724 6  8-12 5 0.17241379 1.034483 5 13-25 13 0.448275862.241379 4 26-29 4 0.13793103 0.551724 29 1 8

Table 6 is a modified version of Table 4, with the fourth stage addedshowing the overall payout percentage of this modified game is 95.43%with all twenty lines played. Also note that the payout percentage onthe fourth stage is 100.34%. A bet on this particular stage has apositive expectation for the player. This bet (on lines sixteen throughtwenty) is only allowed in conjunction with the negative-expectationbets (i.e., less than 100%) on the first fifteen lines, thus resultingin an overall negative expectation of a 95.43% return.

TABLE 6 Multiplier Probability Probability For Pays EV of All of hit onthis of Playing on this EV of EV of This Stages up to Stage stage ThisStage Stage Machine Stage this Level 1 0.517274074 1 1 0.9062397120.906239712 0.906239712 2 0.517274074 0.517274074 2 0.9062397120.937548616 0.921894164 3 0.517274074 0.267572468 4 0.9062397120.969939184 0.937909171 4 0.517274074 0.1384083 8 0.9062397121.003448787 0.954294075

To add even more excitement to the presentation of the foregoing fourthstage, another variation of this four stage game adds a mechanical wheelfor selection of the multiplier for wins on the fourth stage. Adams,U.S. Pat. No. 5,823,874 and U.S. Pat. No. 5,848,932, and Telnaes, U.S.Pat. No. 4,448,419, may be referred to for detail on such bonussequences and indicia. The wheel 42 shown in FIG. 11 has sixteensections, although any number of visible sections may be used. Table 7uses the same multiplier values as shown in Table 5, but allocates thesevalues to the sixteen sections of the mechanical wheel of FIG. 11.

The above-described embodiment of a gaming slot machine having fourstages and a random number multiplier on the fourth stage isoperationally summarized in the flow charts of FIGS. 12A-12C. Theprogram for this Multi-Strike Slots variation embodiment issubstantially the same as that previously described with respect toFIGS. 10A through 10E. Accordingly, and keeping with the same conventionused throughout this application, like numbers are used to describe likesteps. The changes made to the previously-described program willtherefore only be discussed as to this version.

Turning first to FIG. 12A, Multi-Strike Slots follows the sameprogramming as set forth in the flow charts of FIGS. 10A through 10C forTriple-Strike Slots, and up through step 220. Step 232 begins a sequencefor a fourth stage/level/machine, with steps 233, 234, 237 and 238corresponding to steps 183, 184, 187 and 188, respectively, except asnow related to a fourth machine. Note that in the event of no bet on thefourth machine (step 232), a “Game Over” sequence is then engaged atstep 176 c.

As in the other levels, the “Spin Reels” button is once more deactivated(step 239), and steps 240, 241 and 242 a through 242 e repeat steps 169,170 and 171 a through 171 e, respectively, this time for the fourthmachine. Turning to FIG. 12B, steps 245, 247 and 248 then repeat theprocess for the fourth machine described in steps 175, 177 and 178,respectively, with regard to the first machine 18.

Step 249 will now initiate a sequence for a multiplier to be applied tothe fourth level in this version. First, a number is randomly selectedfrom a table provided for the fourth level multiplier at step 249. Thebonus wheel 42 (FIG. 11) may then be graphically “spun” at step 250, andstopped on the previously selected number from step 249, as indicated atstep 253. A mechanical wheel of the type disclosed in U.S. Pat. Nos.5,823,874 and 5,848,932 can likewise be advantageously employed. Thismultiplier factor is then displayed (step 254), and the “Sub-Total”amount for the fourth level is then increased by this factor anddisplayed as a “Total” for the fourth machine (step 255), with thelatter sum then added to the “Total Won” meter 36 amount for display, asshown in step 256. The game then proceeds from step 256 to “Game Over”sequence 176 c. The “Game Over” sequence shown at FIG. 12C for thisversion is the same as that previously described, except for reflectingthe path from point 11 (rather than from point 9 in the previousversion).

TABLE 7 Wheel Stop Multiplier Values Occurrences Probability EV 1 8  1 10.034482759 0.275862069 2 5 2-3 2 0.068965517 0.344827586 3 6 4-6 30.103448276 0.620689655 4 5 7-9 3 0.103448276 0.517241379 5 10 10-11 20.068965517 0.689655172 6 4 12-13 2 0.068965517 0.275862069 7 50 14 10.034482759 1.724137931 8 5 15-17 3 0.103448276 0.517241379 9 25 18 10.034482759 0.862068966 10 4 19 1 0.034482759 0.137931034 11 10 20 10.034482759 0.344827586 12 5 21-23 3 0.103448276 0.517241379 13 8 24 10.034482759 0.275862069 14 4 25 1 0.034482759 0.137931034 15 6 26-27 20.068965517 0.413793103 16 5 28-29 2 0.068965517 0.344827586 29 1 8

Triple-Strike Stud Poker

Another embodiment uses this multi-stage game technique for the play ofvideo poker. This second embodiment adapts a Five-Card Stud game withhit rates under 50% and over 50%. The invention may also be used toadapt many other poker games, including Five-Card Draw poker, DoubleDown Stud poker (see e.g., U.S. Pat. Nos. 5,100,137 and 5,167,413) andBig Split poker (disclosed by the inventors herein in a pending U.S.patent application) among others.

In this second embodiment, there are three stages of Five-Card Studpoker. This game pays on any hand that is one pair or better. It will beseen that about 49.88% of hands in Five-Card Stud poker rank as one pairor higher. For this game with a “hit rate” under 50%, it would beundesirable to use 2× and 4× multipliers on the second and third stagesrespectively, since this would make the return of these stages lowerthan the first stage. This means that a player wagering more money wouldget a lower expected return, which is undesirable to the proprietor ofthe game who wants to encourage as high a wager as possible, but mayalso run afoul of regulations in certain gaming jurisdictions, whichrequire equal or higher return for each coin wagered on a single game.There are many ways that the game may be modified to cause the higherstages to have a higher payout, of which two will be shown here.

In the first version of this poker embodiment, a separate paytable isused for each stage of the game, as shown in FIG. 13. In FIG. 13, it isclear that the Hand #2 (51) paytable has all pays from the Hand #1 (50)paytable multiplied by 2×, except for the “4 of a Kind” which goes from50 to 200, thus providing additional return that will more than offsetthe “hit rate” being under 50%. Likewise, the Hand #3 (52) paytable hasall pays from the Hand #2 paytable multiplied by 2× except for the “FullHouse”, which goes from 50 to 150, which again more than offsets the“hit rate” being under 50%. This will become clear in the analysis shownbelow, if not already evident.

Referring still to FIG. 13, the player uses the “Select Number of Hands”button 54 to select a bet on one to three hands (stages) 50, 51 and 52.The game may be configured with more or less stages (number of hands)without departing from the invention. The “Coins per Hand” button 55 isthen used to wager from one to five coins per hand. This range of coinsmay be modified to any acceptable range, as is well known in the art.The “Deal Hand” button 56 will cause the game to deal out Hand #1 (50)from a standard fifty-two card deck of playing cards. While this gameuses a standard deck of cards of rank and suit, other embodiments mayuse one or more “Jokers.” Still other embodiments may use certain cards,such as Deuces, as wild cards. Even more broadly, while this secondembodiment is a poker game, other card games or different games ofchance will be readily adaptable to use with the overall inventiveconcept, as previously noted.

FIG. 14 shows the game screen after one coin was bet on three hands, anda first stage hand has been dealt. The hand shown contains a pair of5's, which pays one coin for a “Low Pair” (highlighted on the Hand #1(50) paytable). The one coin won is shown in the “Total Won” meter 58.As a result of achieving any win on Hand #1, Hand #2 (51) may now beplayed. If Hand #1 (50) was a loser (less than one pair), then the gamewould be over and the wagers on Hand #2 (51) and Hand #3 (52) would belost without playing those stages.

Having won Hand #1 (50), however, the player presses the “Deal Hand”button 56 and a second hand is dealt as is shown in FIG. 15. In thishand 51, the player has received another pair of 5's, which now pays twocoins as called out in the Hand #2 (51) paytable. The “Total Won” meter58 is updated to three (one coin from Hand 190 1 plus two coins fromHand #2). As a result of a win on Hand #2, Hand #3 (52) may now beplayed. If Hand #2 (51) had been a loser (less than one pair), then thegame would be over and the wager on Hand #3 lost.

The player once again presses the “Deal Hand” button 56 after success atstage two, and a third hand (52) is dealt as is shown in FIG. 16. Thishand has a pair of tens and a pair of deuces for “Two Pair.” Thepaytable shows that two pair pays twelve coins when achieved on Hand #3(as opposed to six coins on hand #2 or three coins on hand #1). The“Total Won” meter 58 is updated to “15,” and the game is over since allhands wagered on have been played. The total win of fifteen credits isadded to the “Credits” meter 59, advancing the meter from “177” to “192”(from an arbitrary start of “180”).

Analysis of Triple-Strike Stud Poker Game

Table 8 shows how the calculation of certain architecture of the payoutpercentage (expected return) of the first stage of this secondembodiment is computed. This table is for a one coin bet. It is wellknown in the art how to expand this for a higher number of coins bet perhand, and for the inclusion of bonuses for a higher number of coins.

The number of possible five card poker hands from a fifty-two card deckis known as “52 choose 5” and is computed with the following formula:

$\frac{52!}{{5!}*{\left( {52\text{-}5} \right)!}} = {2,598,960}$

The first column of Table 8 shows the rank of all hands in thisFive-Card Stud game. The second column shows the pay value for thisranking on Hand #1 (each hand 50, 51 and 52 having a separate paytable).The third column (“Occurrences”) is the number of times a particularhand occurs in the 2,598,960 possible five card poker hands dealt from astandard deck. This “Occurrence” tabulation is well known to thoseskilled in the art, and may be derived by analyzing each of the2,598,960 hands with a computer program, also well known. The fourthcolumn shows the probability of playing Hand #1 when a bet is placed onthis hand. For Hand #1 this probability is 1.0, since the first handwill always be played when it is bet on. The fifth column shows theprobability of receiving the hand called out in the first column. Thisis computed by dividing the “Occurrences” (third column) by the2,598,960 total number of possible hands.

The sixth column is the product of the fourth and fifth columns, whichis the probability of getting a particular hand on this stage (for thefirst stage it is the same as the fifth column since the first stage isalways played). The seventh column is the expected value contributionEV, which is the product of the second column pay and the sixth columnprobability of achieving the given hand on the current stage. The sum ofall EV contributions provides the expected return of 0.916288 or 91.63%.This expected return may be modified by making modifications to the“Pay” values in the second column of Table 8, as is well known in theart.

TABLE 8 Probability of Probability Probability of Playing This of ThisHand on Pay Occurrences Stage This Hand This Stage EV ROYAL FLUSH 2000 41 1.5391E−06 1.53908E−06 0.003078 STRAIGHT FLUSH 250 36 1 1.3852E−051.38517E−05 0.003463 FOUR OF A KIND 50 624 1 0.0002401 0.0002400960.012005 FULL HOUSE 25 3,744 1 0.00144058 0.001440576 0.036014 FLUSH 155,108 1 0.0019654 0.001965402 0.029481 STRAIGHT 8 10,200 1 0.003924650.003924647 0.031397 THREE OF A KIND 5 54,912 1 0.02112845 0.0211284510.105642 TWO PAIR 3 123,552 1 0.04753902 0.047539016 0.142617 JACKS ORBETTER 2 337,920 1 0.13002124 0.130021239 0.260042 LOW PAIR 1 760,320 10.29254779 0.292547788 0.292548 BUST 1,302,540 1 0.50117739 0.5011773940 2,598,960 1 0.916288

Table 9 shows a similar analysis for Hand #2 (51) (the second stage ofthis game).

The second column now has the Hand 190 2 paytable showing all valuesdoubled from the Hand #1 paytable with the Four of a Kind going from 50to 200. The fourth column, “Probability of Playing This Stage” is theprobability of getting any “hit” (one pair or higher) on the firststage. This is computed by adding up all of the fifth column values fromTable 8 except for “Bust,” or by subtracting the probability of a “Bust”(0.50117739) from 1.0, resulting in a first stage hit rate of0.498822606 or 49.88%. The sum of the EV components on the second stageis 0.9261078, indicating a 92.61% expected return. This higher expectedreturn than the first stage is a result of the 200 coin Four of a Kindvalue more than offsetting the “hit rate” which is slightly under 50%.This expected return may, again, be modified by making modifications tothe “Pay” values.

TABLE 9 Probability of Probability Probability of Playing This of ThisHand on Pay Occurrences Stage This Hand This Stage EV ROYAL FLUSH 4000 40.498822606 1.5391E−06 7.67726E−07 0.003071 STRAIGHT FLUSH 500 360.498822606 1.3852E−05 6.90954E−06 0.003455 FOUR OF A KIND 200 6240.498822606 0.0002401 0.000119765 0.023953 FULL HOUSE 50 3,7440.498822606 0.00144058 0.000718592 0.03593 FLUSH 30 5,108 0.4988226060.0019654 0.000980387 0.029412 STRAIGHT 16 10,200 0.498822606 0.003924650.001957703 0.031323 THREE OF A KIND 10 54,912 0.498822606 0.021128450.010539349 0.105393 TWO PAIR 6 123,552 0.498822606 0.047539020.023713536 0.142281 JACKS OR BETTER 4 337,920 0.498822606 0.130021240.064857533 0.25943 LOW PAIR 2 760,320 0.498822606 0.29254779 0.145929450.291859 BUST 1,302,540 0.498822606 0.50117739 0.249998614 0 2,598,960 10.926107

Table 10 shows a similar analysis for Hand #3 (52) (the third stage ofthis game). The second column now has the Hand #3 paytable showing allvalues doubled from the Hand #2 paytable with the Full House going from50 to 150. The “Probability of Playing This Stage” is the probability ofgetting any “hit” (one pair or higher) on the first and second stages.This is the square of the 0.498822606 “hit rate” of the first stagesince a “hit” is required on both the first and second stages in orderto play the third stage. The fourth column value may also be computed bysubtracting the probability of getting a “Bust” on the first stage(0.50117739) and the probability of getting a “Bust” on the second stage(0.249998614) from 1.0 (i.e., 1−0.50117739−0.249998614=0.248823992). Thesum of the EV components on the third stage is 0.941849, indicating a94.18% expected return. This higher expected return than the secondstage likewise is a result of the 150 coin Full House value more thanoffsetting the second stage “hit rate” which is slightly under 50%. Onceagain, the expected return may be modified by making modifications tothe “Pay” values.

TABLE 10 Probability of Probability Probability of Playing This of ThisHand on Pay Occurrences Stage This Hand This Stage EV ROYAL FLUSH 8000 40.248823992 1.5391E−06 3.82959E−07 0.003064 STRAIGHT FLUSH 1000 360.248823992 1.3852E−05 3.44663E−06 0.003447 FOUR OF A KIND 400 6240.248823992 0.0002401 5.97417E−05 0.023897 FULL HOUSE 150 3,7440.248823992 0.00144058 0.00035845 0.053767 FLUSH 60 5,108 0.2488239920.0019654 0.000489039 0.029342 STRAIGHT 32 10,200 0.248823992 0.003924650.000976546 0.031249 THREE OF A KIND 20 54,912 0.248823992 0.021128450.005257266 0.105145 TWO PAIR 12 123,552 0.248823992 0.047539020.011828848 0.141946 JACKS OR BETTER 8 337,920 0.248823992 0.130021240.032352404 0.258819 LOW PAIR 4 760,320 0.248823992 0.292547790.072792909 0.291172 BUST 1,302,540 0.248823992 0.50117739 0.12470496 02,598,960 1 0.941849

Table 11 shows the return of betting on one, two or three stages in thispoker game of the second embodiment. For the “Stage” called out in thefirst column, the second column shows the EV for that stage taken fromTables 8, 9, and 10. The third column is the EV of an entire multi-stagegame with a bet on the number of stages in the first column. This is theaverage of the selected second column level and all levels above (i.e.,the average EV of all those stages in the multi-stage game). Theexpected return of the entire game when a player plays all three stagesis 0.928081203 or 92.81%.

TABLE 11 EV of Game Total EV Playing this many Stage For Stage stages 10.91628805 0.916288054 2 0.92610692 0.921197488 3 0.94184863 0.928081203

A Variation on Triple-Strike Stud Poker

This modification of the Triple-Strike Stud poker game introduces a“Free Ride” feature. This feature is used to increase the “hit rate” ofthe basic game without making any other modifications to the game (suchas which hands pay). This feature provides a greater flexibility insetting the “hit rate” than is available by simply setting which rank isthe lowest pay. Using normal poker game construction techniques, onewould typically have to include more paying hands to increase the “hitrate.” In the game of the above second embodiment, the highest nonpayinghand to add would be “Ace High,” which would add almost 20% to the hitrate as shown in Table 12. Paying on all hands that have an Ace(referred to as “Ace High”) would bring the hit rate up from 49.88% to69.23%, which is far beyond the goal of just over 50%. Another variancecould require “Ace-King” high as the minimum hand, which would bring thehit rate to 56.32%, which is still a very large increase.

TABLE 12 Sum of Hit Rate at Occurrences Occurrences this rank ROYALFLUSH 4 4 0.00% STRAIGHT FLUSH 36 40 0.00% FOUR OF A KIND 624 664 0.03%FULL HOUSE 3744 4408 0.17% FLUSH 5108 9516 0.37% STRAIGHT 10200 197160.76% THREE OF A KIND 54912 74628 2.87% TWO PAIR 123552 198180 7.63%JACKS OR BETTER 337920 536100 20.63% LOW PAIR 760320 1296420 49.88%ACE-KING 167280 1463700 56.32% ACE HIGH 335580 1799280 69.23% BUST799680 2598960 100.00% 2,598,960

In this modified embodiment, a “Free Ride” feature is added to the gamewherein in some of the hands, on a random basis, a “Free Ride” indiciawill be displayed, advantageously with an accompanying sound. When the“Free Ride” is indicated, the hand will be dealt as usual and paidaccording to the paytable, but the game will automatically advance tothe next hand that was wagered on, whether or not the player wins thecurrent hand.

Using this feature, multiple stages of this game can be constructed witha natural hit rate under 50%, yet use the same paytable for all stageswith multipliers for each stage.

Another advantage of the “Free Ride” feature is that it is not necessaryto modify paytable values to increase the “hit rate.” It is well knownin the art that as additional “pays” are allowed to increase the “hitrate,” other pay values or frequencies will need to be decreased tooffset the amount paid out on the new values. The “Free Ride” introducesa method of raising the “hit rate” of a game without any othermodification to the payout of the game through the use of “hits” thataward no coins/credits. This is important for the purpose of adaptinggames with paytables that are already familiar to the players. It isalso a valuable tool that gives the game designer more flexibility inthe creation of a game.

Table 8 is still representative of the first stage of this “Free Ride”version. In this modified embodiment, the “Free Ride” is offered onsixteen of every one thousand hands (based on a random number for eachhand), or 1.6% of the hands played. This will increase the “hit rate” ofthe stage. Using more than 1.6% “Free Rides” will provide a greaterincrease, while using less than 1.6% will provide a smaller increase inthe “hit rate.” Because the “Free Ride” offers no benefit when playingon the highest hand that has been wagered on (there being no “next hand”to advance to) it is not offered on the final hand.

Table 13 shows how the “hit rate” is determined for the first stage ofTable 8 that includes a 1.6% “Free Ride.” The first line shows the “hitrate” that is achieved for first stage hands, 0.4988. The second lineshows the sixteen in one thousand probability of the “Free Ride” beingoffered. The third line shows the probability of losing on the firststage. This is the “Bust” probability taken from Table 8. The fourthline is the product of the second and third lines, showing theprobability of getting a “Free Ride” on a “Busted” hand. This is theadditional “hit rate” component, since winning hands that receive theFree Ride are already figured into the first line. The fifth line is thesum of the first and fourth lines and is the resulting “hit rate” forthe first stage including the “Free Ride” feature which is 0.506841 or50.68%.

TABLE 13 Hit Rate for Hands of First Stage 0.498823 Free Ride Prob.0.016 First Stage Busts 0.501177 Free Ride Hits 0.008019 First Stage HitRate w/ Free Ride 0.506841

The second stage of the “Free Ride” variation is now represented byTable 14, which is similar to Table 9. The differences are in the “Pay”values, which are now exactly twice (2× multiplier) the “Pay” valuesfrom Table 8, and the fourth column “Probability of Playing This Stage”,which is now the 0.506841 value, computed in Table 13.

TABLE 14 Probability of Probability Probability of Playing This of ThisHand on Pay Occurrences Stage This Hand This Stage EV ROYAL FLUSH 4000 40.506841444 1.5391E−06 7.80068E−07 0.00312 STRAIGHT FLUSH 500 360.506841444 1.3852E−05 7.02061E−06 0.00351 FOUR OF A KIND 100 6240.506841444 0.0002401 0.000121691 0.012169 FULL HOUSE 50 3,7440.506841444 0.00144058 0.000730144 0.036507 FLUSH 30 5,108 0.5068414440.0019654 0.000996147 0.029884 STRAIGHT 16 10,200 0.506841444 0.003924650.001989174 0.031827 THREE OF A KIND 10 54,912 0.506841444 0.021128450.010708775 0.107088 TWO PAIR 6 123,552 0.506841444 0.047539020.024094743 0.144568 JACKS OR BETTER 4 337,920 0.506841444 0.130021240.065900153 0.263601 LOW PAIR 2 760,320 0.506841444 0.292547790.148275344 0.296551 BUST 1,302,540 0.506841444 0.50117739 0.254017474 02,598,960 1 0.928826

The third stage for the “Free Ride” variation is represented by Table15, which is similar to Table 10. Again, the differences are in the“Pay” values, which are now exactly twice (2× multiplier), the “Pay”values from Table 14, and the fourth column “Probability of Playing ThisStage”, which is now 0.25688825, which is the square of the 0.506841“hit rate” of the first stage.

TABLE 15 Probability of Probability Probability of Playing This of ThisHand on Pay Occurrences Stage This Hand This Stage EV ROYAL FLUSH 8000 40.25688825 1.5391E−06 3.95371E−07 0.003163 STRAIGHT FLUSH 1000 360.25688825 1.3852E−05 3.55834E−06 0.003558 FOUR OF A KIND 200 6240.25688825 0.0002401 6.16779E−05 0.012336 FULL HOUSE 100 3,7440.25688825 0.00144058 0.000370067 0.037007 FLUSH 60 5,108 0.256888250.0019654 0.000504889 0.030293 STRAIGHT 32 10,200 0.25688825 0.003924650.001008196 0.032262 THREE OF A KIND 20 54,912 0.25688825 0.021128450.005427651 0.108553 TWO PAIR 12 123,552 0.25688825 0.047539020.012212215 0.146547 JACKS OR BETTER 8 337,920 0.25688825 0.130021240.033400929 0.267207 LOW PAIR 4 760,320 0.25688825 0.292547790.075152089 0.300608 BUST 1,302,540 0.25688825 0.50117739 0.128746584 02,598,960 1 0.941535

Finally, Table 16 is a similar table to Table 11, showing the overallpayout percentage of the one, two and three stage versions of this “FreeRide” game. The increase in overall payout is a little over 1.2% whengoing from one to three stages. This range may be increased using ahigher “Free Ride” percentage, or decreased using a lower “Free Ride”percentage. One skilled in the art will appreciate that changing thepayout range using this independent “Free Ride” percentage provides muchbetter precision and flexibility for setting this range than thepaytable modification method used in the unmodified second embodiment.

TABLE 16 EV of Game Total EV Playing this many Stage For Stage stages 10.91628805 0.916288054 2 0.92882552 0.922556787 3 0.94153454 0.928882704

Multi-Strike Five-Card Draw Poker

Five-Card Draw poker is a very popular casino game and is offered inmany variations including Jacks or Better, Joker Poker, Deuces Wild andvarious “bonus” type Jacks or Better versions, among others. While it iswithin the scope of the invention to use any poker game with paytablesand/or multipliers that provide the increased reward on the higherstages, or to use different variations of poker or even other games ofchance on different levels, this third embodiment will use a well knowngame with its well known paytables. It will also use multipliers toincrease the reward on the higher levels.

Many of the popular Five-Card Draw poker games have hit rates in the 40%to 50% range, including Jacks or Better, Deuces Wild and the many“bonus” poker variations that are popular today in the marketplace.Since most gaming jurisdictions require that video poker be played froma “fair” deck of cards, it has become widely known that a player candetermine the payout percentage of a video poker machine by looking atits paytable. This has resulted in a growing popularity of this type ofgame. In this embodiment of the invention, a multiple stage Five-CardDraw poker game is constructed, also using the “Free Ride” featurepreviously discussed to maintain the familiar paytable. It will be shownthat the frequency of the “Free Ride” feature can be used to achieve asimilar payout percentage in the multi-stage game as the player mayexpect from the familiar paytable.

FIG. 17 shows the current (third) embodiment four-stage 9-6 Jacks orBetter game. The game uses the familiar paytable shown in FIG. 18, whichmay be displayed by pressing the “Pay Table” button 65 shown in FIG. 17.The player presses the “Select Number of Hands” button 66 to designate abet on one to four hands (stages) of this game. This third embodiment ofcourse may be constructed with a lesser or greater number of stages thanfour, without departing from the invention.

The player presses the “Coins per Hand” button 67 to select a betranging from one to five coins per hand. Those skilled in the artunderstand how to allow the range of coins bet to be broader or narroweror how to add bonuses for higher bets.

The “Total Bet” is the product of the “Select Number of Hands” and“Coins per Hand” values, and is displayed in the “Total Bet” window 68.The player then presses the “Deal/Draw” button 70 to deal out a hand onthe first stage 71. The buttons shown in FIG. 17 are video buttons foruse with a touchscreen display. A pointing device such as a mouse ortrackball, physical pushbutton switches and the like may be used inaddition to or instead of the video buttons shown. If the player wishesto bet the maximum twenty coins on a game, he or she may press the “MaxBet Deal” button 76 which has the same result as pressing the “SelectNumber of Hands” button 66 until “4” is shown, followed by pressing the“Coins per Hand” button 67 until “5” is shown, followed by pressing the“Deal/Draw” button 70.

After receiving the initial hand, the player may hold one or more cardsby using the touchscreen to indicate which cards are to be discarded.FIG. 19 shows the display after the player elects to hold only the Jackof Spades 80 from the hand dealt in FIG. 17. FIG. 19 shows the word“Held” above the Jack of Spades 80 that was selected to be held. Theplayer then presses the “Deal/Draw” button 70 to replace the other fourcards.

FIG. 20 shows a possible result of the draw. The draw results in a Threeof a Kind. The Three of a Kind awards three coins as shown in the FIG.18 paytable. The three coin award multiplied by the Hand #1 (71)multiplier of 1× is shown to total three coins in the first stage payoutinformation window 84 to the right of Hand #1 in FIG. 20. This threecoin sub-total is shown in the “Total Won” meter 85 of FIG. 20. If Hand#1 was a loser instead of getting “Jacks or Better” (as was accomplishedwith a hand of Three of a Kind), the game would be over and the bets onHand #2 (72), Hand #3 (73) and Hand #4 (74) would be lost withoutplaying those hands.

However, as a result of obtaining a winning hand, the bet made on Hand#2 (72) will now be played. Five cards are dealt randomly from aseparate (new) deck of fifty-two cards in the Hand #2 position. FIG. 20shows that the cards dealt to Hand #2 (72) include a pair of Queens 81,which already ranks above the “Jacks or Better” level required to win. Askilled player would hold the pair of Queens, and press the “Deal/Draw”button 70.

FIG. 21 shows one possible result of this second draw. In FIG. 21, athird

Queen was drawn to Hand #2 resulting in Three of a Kind, which as seenon Hand #1, awards three coins. FIG. 21 shows that this three coin awardis multiplied by the 2× multiplier for Hand #2, which results in a sixcoin total win from Hand #2. The coins awarded are shown in the secondstage payout information window 87 to the right of Hand #2 (72). The“Total Won” meter 85 is now updated to show nine coins won, which is thesum of the three coins won on Hand #1 and the six coins won on Hand #2.If Hand #2 was a loser instead of getting “Jacks or Better” (as wasaccomplished with a hand of Three of a Kind), the game would be over andthe bets on higher level hands would be lost.

Since a winning hand was achieved on Hand #2, the bet made on Hand #3(73) will now be played. Five cards are again dealt randomly from a newdeck in the Hand #3 position (73). FIG. 21 shows that the cards dealt toHand #3 include two pair, which already is above the “Jacks or Better”level required to win. A skilled player would hold the two pair andpress the “Deal/Draw” button 70.

FIG. 22 shows one possible result of this third draw. In FIG. 22, Hand#3 was not improved, resulting in two pair which awards two coins. FIG.22 shows that this two coin award is multiplied by the 4× multiplier forHand #3, which results in an eight coin total win from Hand #3. Thesenumbers are shown in the third stage payout information window88 to theright of Hand #3 (73). The “Total Won” meter 85 is now updated to showseventeen coins won, which is the sum of the three coins won on Hand 1901, the six coins won on Hand #2 and the eight coins won on Hand #3.

As a result of obtaining a winning hand on Hand #3, the bet made on Hand#4 (74) will now be played. Five cards are again dealt randomly from anew deck in the Hand #4 (74) position. FIG. 22 shows that the cardsdealt to Hand #4 include three Jacks, which already is above the “Jacksor Better” level required to win. The three Jacks are held by the playerand the “Deal/Draw” button 70 is again pressed.

FIG. 23 shows one possible result of this fourth draw. In FIG. 23, Hand#4 (74) becomes a Full House as a result of drawing a pair of fours. AFull House awards nine coins as seen in FIG. 18. FIG. 23 shows that thisnine coin award is multiplied by the 8× multiplier for Hand #4, whichresults in a seventy-two coin total win from Hand #4. These numbers areshown to the right of Hand #4 (74) in the fourth stage payoutinformation window 89. The “Total Won” meter is now updated to showeighty-nine coins won which is the sum of coins won on all levels. Thegame is over as a result of playing all hands on which bets were placed.The credits shown in the “Total Won” meter 85 are added to the “TotalCredits” window 77 taking this value to “285.”

Multi-Strike Five-Card Draw Poker with “Free Ride”

In another example of the foregoing embodiment of Five-Card Draw poker,the same “Free Ride” feature that was described for Five-Card Stud pokeris used to increase the hit rate without having to modify the popularlyknown paytable. FIG. 24 shows that the “Free Ride” card 90 was dealt tothe player in Hand #1 (71). The game makes an exciting sound when thecard is dealt to alert the player that Hand #2 (72) will be availablewhether or not a win is achieved on Hand #1. After showing the FIG. 24display for a few seconds to allow the special sound to complete, the“Free Ride” card 90 is replaced by another randomly selected card andthe remainder of the hand is dealt to the player in usual fashion.

FIG. 25 shows this completed hand along with a “Free Ride” indicator 91on the left edge of the screen. As in the previous example, the playerwill hold desired cards and draw replacements for those cards not held.A skilled player would hold the 7, 10 and Jack of Diamonds, and thenpress the “Deal/Draw” button 70.

FIG. 26 shows that the cards drawn did not result in a win. The firststage payout information window 84 now shows a zero coin win with “FreeRide” being indicated as the reason for advance. As a result of the“Free Ride” on Hand #1 (71), five cards are now dealt for Hand #2 (72).Play would continue from level to level as long as there is a winninghand, or “Free Ride” on each level, as previously described.

Analysis of Certain Architecture of the Multi-Strike Five-Card DrawPoker Game

Part I—Review of “Standard Video Poker”

This analysis is of a “standard video Draw poker” game, which will thenbe related to Multi-Strike Five-Card Draw poker for a one coin wager perhand. It is well known by those skilled in the art how to expand this tomore coins bet, and how to add bonuses for higher bets.

Those skilled in the art of video poker development know that a FiveCard Draw poker game with the paytable shown in Table 17 has an expectedreturn of 99.54398%. This payout percentage is what the game will returnin the long run with “Optimal Play”. This game is usually referred to as9-6 Jacks or Better. This is because most Jacks or Better games (withoutFour-of-a-Kind bonuses) use the same paytable except for the Full Houseand Flush awards which are modified to change the payout percentage. Itis well known that a 9-6 Jacks or Better (awarding nine coins for FullHouse and six coins for Flush) provides a 99.54% return.

TABLE 17 Hand Rank Pay Occurrences Probability EV Royal Flush 80064.3457483 2.47583E−05 0.019806614 Straight Flush 50 284.14101730.000109329 0.005466437 Four of a Kind 25 6140.161736 0.0023625460.059063642 Full House 9 29919.76638 0.011512207 0.103609866 Flush 628626.22236 0.011014491 0.066086948 Straight 4 29184.62522 0.0112293480.04491739 Three of a 3 193489.1896 0.074448699 0.223346096 Kind TwoPair 2 335990.6964 0.129278902 0.258557805 Jacks or Better 1 557697.91250.214585031 0.214585031 Bust 0 1417562.939 0.545434689 0 2598960 10.99543983

Unlike the previous embodiments, Draw poker has a skill element thatrequires decisions by the player on each hand. The game is designed suchthat the payout percentage will be reached over the long run when thegame is played optimally. Each non-optimal play lowers the expectedreturn (although it could result in a higher short term result). Each ofthe 2,598,960 possible hands may be played thirty-two ways by holdingnone, or any combination of the five initial cards dealt. Using expectedvalue analysis of the thirty-two combinations can determine the bestplay for any given hand. One skilled in the art is readily able toconstruct the table in Table 17 by writing a computer program thatperforms this analysis on each of the 2,598,960 hands.

To further clarify this method, one of the possible 2,598,960 hands isexamined, and in particular, the hand shown in FIG. 19: Jack of Spades,10 of Hearts, 9 of Diamonds, 8 of Clubs and 4 of Hearts. To find thebest way to play a hand, one computes the expected value of each of thethirty-two ways to play the hand. Here, two of the thirty-two ways tohold the hand of FIG. 19 are analyzed. In one case, the Jack-10-9-8 fourcard straight is held. The second case will be holding just the Jack ofSpades.

Table 18 shows the expected return for holding the Jack-10-9-8 four cardstraight. The first two columns show all possible rankings and their payvalue. The third column shows the number of occurrences of each of thesepossible ranks when drawing to this exact situation (i.e., given theinitial five cards, the cards that were held and the suits and rank ofthe remaining forty-seven cards). The computation of this third columnmay be exhaustively determined by analyzing each possible resultinghand, but is usually done by an analysis of the combinations of the heldand remaining cards, which may be computed more quickly. In this exampleof drawing one card, it is easy to see that any of the four outstandingQueens or 7's result in eight possible straights, and the threeoutstanding Jacks would result in a pair of Jacks. All other draw cardswould result in a “Bust”. The fourth column shows the “Probability” ofdrawing to the specified rank, which is computed by dividing the thirdcolumn “Occurrences” count by the forty-seven total ways to draw thishold combination. The fifth column “EV” is the product of the “Pay”value of second column and the “Probability” value of fourth column. Thesum of EV components results in a 0.744681 expected return for thisplay. That is, on average, this hold will yield 74.47% of the amount betin the long run.

TABLE 18 (Expected Value of Holding Jack-10-9-8 from the FIG. 19 Hand)Hand Rank Pay Occurrences Probability EV Royal Flush 800 0 0 0 StraightFlush 50 0 0 0 Four of a Kind 25 0 0 0 Full House 9 0 0 0 Flush 6 0 0 0Straight 4 8 0.17021277 0.680851 Three of a Kind 3 0 0 0 Two Pair 2 0 00 Jacks or Better 1 3 0.06382979 0.06383 Bust 0 36 0.76595745 0 47 10.744681

Table 19 shows a similar analysis for the case where just the Jack isheld from the same hand shown in FIG. 19. The “Occurrences” column now,involves 178,365 different resulting hands when only 1 card is held.This number of combinations is “47 choose 4” which is stated by theformula:

$\frac{47!}{{4!}*{\left( {47\text{-}4} \right)!}} = {178,365}$

This specifies the number of combinations of forty-seven cards takenfour cards at a time. As stated above, these “Occurrences” are found bya well known/readily obtained computer program that either exhaustivelyanalyzes each of the 178,365 draw combinations in conjunction with theJack of Spades, or by an analysis of the combinations of the held andremaining cards. The expected return of holding the Jack of Spades iscomputed in Table 19 in a manner similar to that used in Table 18,resulting in a 47.93% expected return in the long run. Analyzing theother thirty ways to play this hand results in an even lower expectedreturn than the “Jack Hold” of Table 19. Therefore, the best play forthis particular hand is to hold the four card Straight analyzed in Table18.

TABLE 19 (Expected Value of Holding Only the Jack in FIG. 19 Hand) HandRank Pay Occurrences Probability EV Royal Flush 800 1 5.60648E−060.004485 Straight Flush 50 3 1.68194E−05 0.000841 Four of a Kind 25 520.000291537 0.007288 Full House 9 288 0.001614667 0.014532 Flush 6 4910.002752782 0.016517 Straight 4 548 0.003072352 0.012289 Three of a Kind3 4102 0.022997785 0.068993 Two Pair 2 8874 0.049751913 0.099504 Jacksor Better 1 45456 0.254848205 0.254848 Bust 0 118550 0.664648333 0178365 1 0.479298

The analysis program that iterates over each of the 2,598,960 handsfinds the best of the thirty-two possible holds, and keeps a running sumof the expected return for these optimal holds (for the sample hand ofFIG. 19, 0.744681 would be added to this sum). The sum of all optimalhold expected returns is then divided by 2,598,960 to determine theexpected return for the game. The fifth column of Table 17 shows thisresult of 0.99543983 along with the contribution from each type of hand.

Part II—Modification of Analysis for Multi-Strike Game

In playing a multi-stage Draw Poker game of the present invention, theoptimal hold is no longer necessarily the hold that will provide thehighest expected return for the current hand, but is rather the holdthat will provide the highest expected return on the remainder of themulti-stage game (including the current hand). As with standard Drawpoker, the expected return of thirty-two hold combinations must beexamined. The expected return of any hold combination now has twocomponents. The first component is the expected return of the currenthand (which is the expected return as calculated in Table 18, times thecurrent stage multiplier). The second component is the expected returnof the remainder of the game given that hold combination. The secondcomponent is the product of the “Probability” of any win on the currentstage (for the current hold combination) and the expected return ofremaining stages. This sum may be represented as:

EV _(ch)=(EV _(std) *MULT _(stage))+(HR _(ch) *EV _(remain));   EQUATION1

where

-   -   EV_(ch)=Expected Value of current hold;    -   EV_(std)=Expected Value using standard analysis such as done in        Table 18;    -   MULT_(stage)=Stage Multiplier, which is a constant for each        stage;    -   HR_(ch)=“Hit rate” (probability of any win) of current hold        combination; and    -   EV_(remain)=Combined expected return of all stages above the        current level that have received a bet, which is a constant for        each stage.

Simply stated, the second component is the value of “staying alive” bygetting any win. For certain hands at certain stages, it will beadvantageous to hold a combination with a lower EV_(std) due to itshigher HR_(ch).

The EV_(remain) component drives an analysis of the game from the “topdown.” That is, for games with four stages bet, the analysis is done forthe fourth stage, then using the result from the fourth stage to set theEV_(remain) value, the analysis may be done for the third stage and soon. For each stage, EV_(remain) is a constant value determined from theanalysis of the stage above it.

For the fourth stage, the second component of the Equation 1 sum dropsout, because EV_(remain) is zero since there are no subsequent stages.This means that the EV_(ch) for any given hold is eight times EV_(std),which means that standard 9-6 strategy is optimal, and will provide areturn of 0.99543983*8=7.96351864.

Before looking at the third stage analysis, it is important tounderstand the effect of the “Free Ride” feature. For the examples givenhere, a “Free Ride” rate of seventy-three per one thousand hands isused, or 7.3%. This value was carefully selected to arrive at a total“hit rate” (natural plus “Free Ride”) of slightly over 50%, as will beshown later. Those skilled in the art will see that this rate may beincreased or decreased as desired to affect the “hit rate” and expectedreturn. The “Free Ride” is randomly selected for 7.3% of the hands whenthere is a bet on a higher hand. On hands that receive a “Free Ride”card, the second component of the Equation 1 sum becomes a constant,since HR_(ch) is 1.0 for all holds (i.e., one will “hit” or advance tothe next level 100% of the time regardless of the hold combination).This means that the best hold combination for hands that have been givena “Free Ride” will match the standard strategy.

To analyze the first three stages, one looks at each of the 2,598,960possible initial five card hands. For each hand, the thirty-two possiblehold combinations will need to be analyzed to determine the best EV_(ch)hold using Equation 1 and the best standard play hold using the methodof Table 18 (EV_(std)). For many hands, the same hold will yield thehighest EV_(ch) and the highest EV_(std). The expected return for agiven initial hand is now given by Equation 2:

EV ₁₂₃=(FR _(off) *EV _(chbest))+(FR _(on)*((EV _(stdbest) *MULT_(stage))+(1.0*EV _(remain))));   EQUATION 2

where

-   -   EV₁₂₃=Expected return for a given initial hand on Levels 1, 2 or        3;    -   FR_(off)=Probability of not receiving “Free Ride” (0.927 for        this example);    -   EV_(chbest)=EV_(ch) from hold that yields highest value in        Equation 1;    -   FR_(on)=Probability of receiving “Free Ride” (0.073 for this        example);    -   EV_(stdbest)=EV of best hold combination using standard        (Table 18) analysis;    -   MULT_(stage)=Stage Multiplier, which is a constant for each        stage; and    -   EV_(remain)=Combined expected return of all stages above the        current level that have received a bet, which is a constant for        each stage.

The first component of Equation 2 represents the hands that do notreceive a “Free Ride.” The “No Free Ride” probability of 0.927 is usedto weight the expected return that is computed using the formula ofEquation 1. The second component represents the hands that receive a“Free Ride. The “Free Ride” probability of 0.073 is used to weight thereturn that will result by using the standard 9-6 strategy when a “FreeRide” is awarded on this hand.

For Levels one through three, the expected return is computed by addingthe EV₁₂₃ values for each of the 2,598,960 possible starting hands anddividing by 2,598,960. This expected return has the return of levelsabove it embedded within its value.

It is helpful to look at how EV_(chbest) is found for a particular hand.For the hand shown in FIG. 19, we now use the data from Table 18 andTable 19 to compare the Ev_(ch) for the hold of the four card Straightvs. holding the Jack on the third stage. To do this we use Equation 1:

EV _(ch)=(EV _(std) *MULT _(stage))+(HR _(ch) *EV _(remain))  [EQUATION1]

Taking the Hit Rate (HR_(ch)) for holding Jack-10-9-8=1−(36/47)=0.234043(from Table 18):

Hold Jack-10-9-8: EV_(ch)=(0.744681*4)+(0.234043*7.96351864)=4.84253.

The Hit Rate (HR_(ch)) for Holding Jack=1-(118550/178365)=0.335352 (fromTable 19).

Hold Jack: EV_(ch)=(0.479298*4)+(0.335352*7.96351864)=4.58777.

The EV_(ch) for the other thirty hold combinations is lower than forholding just the Jack, therefore, EV_(chbest)=4.84253 resulting fromholding the four card Straight. From Table 18 and Table 19 it can beseen that EV_(stdbest)=0.744681 for this hand (also hold the straight).Therefore, the expected return on the third stage of this initialfive-card hand is:

EV ₁₂₃=(FR _(off) *EV _(chbest))+(FR _(on)*((EV _(stdbest) *MULT_(stage))+(1.0*EV _(remain)))) [using EQUATION 2]

EV ₁₂₃=(0.927*4.84253)+(0.073*((0.744681*4)+(1.0*7.96351864)))=5.287809

The sum of all of the EV₁₂₃ values divided by 2,598,960 for the thirdstage results in an expected return of 7.95080267. This is the number ofcoins expected to be won in the remainder of any game that reaches thethird stage (i.e. return of third and fourth stages combined).

The second stage is analyzed identically as the third stage, howeverEV_(remain) is now 7.95080267 and MULT_(stage) is now 2. Looking at thehand of FIG. 19, one now has the following calculations:

Hold Jack-10-9-8: EV _(ch)=(0.744681*2)+(0.234043*7.95080267)=3.3501917

Hold Jack: EV _(ch)=(0.479298*2)+(0.335352*7.95080267)=3.6249136

When the hand of FIG. 19 is analyzed on the second stage, it is nowbetter to hold just the Jack rather than Jack-10-9-8, thereforeEV_(chbest) is 3.6249136. The EV_(stdbest) is still 0.744681 asJack-10-9-8 is the best standard play on any stage of the game. Theexpected return of this hand on the second level (including the expectedreturn of levels three and four) EV₁₂₃ for this hand is computed as:

EV ₁₂₃=(0.927*3.624914)+(0.073*((0.744681*2)+(1.0*7.95080267)))=4.049427

A computer program known to those of skill in the art is used to findthat the sum of all of the EV₁₂₃ values divided by 2,598,960 for thesecond stage results in an expected return of 5.96916633. This is thenumber of coins a player is expected to win in the remainder of any gamethat reaches the second stage (i.e. return of second, third and fourthstages combined).

The first stage is analyzed identically as the second and third stages,however EV_(remain) is now 5.96916633 and MULT_(stage) is now 1. Lookingat the hand of FIG. 19, we now have the following calculations:

Hold Jack-10-9-8: EV _(ch)=(0.744681*1)+(0.234043*5.96916633)=2.141723

Hold Jack: EV _(ch)=(0.479298*1)+(0.335352*5.96916633)=2.481070

When the hand of FIG. 19 is analyzed on the first stage, it is againbetter to hold just the Jack rather than Jack-10-9-8, thereforeEV_(chbest) is 2.481070. The EV_(stdbest) is still 0.744681 asJack-10-9-8 is the best standard play on any stage of the game. Theexpected return of this hand on the first level (including the expectedreturn of levels two, three and four) EV₁₂₃ for this hand is computedas:

EV ₁₂₃=(0.927*2.481070)+(0.073*((0.744681*1)+(1.0*5.96916633)))=2.790063

The sum of all of the EV₁₂₃ values divided by 2,598,960 for the firststage results in an expected return of 3.995391. This is the number ofcoins a player is expected to win in a four stage game for which a fourcoin bet is made. Dividing this value by the four coin bet results in anexpected return of 0.998848 or 99.88%. By setting the “Free Ride”percentage at 7.3% for the four stage game, the expected return of99.54% of this standard game was increased to 99.88% to give a player anincentive to learn the modified optimal play strategy dictated by theEV_(ch) analysis.

In order to determine the actual amount paid out on each level as wellas the independent return of coins bet on that level, it is useful tomaintain several running sums while working through each of the2,598,960 possible hands. The following equation is calculated for eachhand, and a sum of these values is maintained:

EV _(playedhand)=(FR _(off) *EVSTD _(chbest))+(FR _(on) *EV_(stdbest))  EQUATION 3

-   -   EV_(stdbest)=EV of best hold combination using standard        (Table 18) analysis    -   EVSTD_(chbest)=Standard (Table 18) analysis EV of best hold for        maximizing Equation 1.

For each hand, if there is no “Free Ride”, it will be held to maximizeEV_(ch) using Equation 1. The FR_(off) value is used to weight thestandard (Table 18 method) EV of this best hold (calledEVSTD_(chbest))). If there is a “Free Ride”, then the optimal play is tohold the combination that gives the highest standard EV. The FR_(on) isused to weight this value. For the example hand of FIG. 19, on the firststage or second stage, this would give the following equation:

EV _(playedhand)=(FR _(off) *EVSTD _(chbest))+(FR _(on) *EV _(stdbest))[using EQUATION 3]

EV _(playedhand)=(0.927*0.479298)+(0.073*0.744681)=0.498671

The EVSTD_(chbest) and EV_(stdbest) values come from Table 19 and Table18, respectively.

For each stage, for each of the 2,598,960 hands, these EV_(playedhand)components are added together and the sum is divided by 2,598,960. Thisindicates the payout of hands played on that level. These values areshown in the second column of Table 20.

In a manner similar to Equation 3, the HR_(ch) hit rate components areweighted and added to result in the hit rate shown in the third columnof Table 20. The fourth column of Table 20 shows the probability ofplaying a hand on a given level, which is 1.0 on the first level, andfor the other levels, is the product of the third and fourth columns ofthe level below. The fifth column shows the stage multiplier for thegiven level. The sixth column is the actual return for a particularlevel, which is the product of the second, fourth and fifth columns. Theseventh column is expected return for the rest of a game that hasreached the current stage. For the fourth stage, this is the product ofthe second column (return) and fifth column (multiplier). For the lowerlevels, it is the product of the second and fifth columns (whichrepresents the Expected Pay for playing the current level) plus thethird column (hit rate on current level) times the seventh column of thenext higher level. This seventh column value is the same as the sum ofthe EV₁₂₃ values previously discussed.

TABLE 20 Payout of Hands played Return for on this Hit Rate Probabilityof Bets on this Level Level of Level Playing Level Multiplier LevelEV_(remain) 4 0.99543983 0.45456531 0.128598042 8 1.024092903 7.963518643 0.99142626 0.5004192 0.256980631 4 1.019109383 7.950802667 20.97183568 0.50630045 0.50756548 2 0.986540487 5.969166328 1 0.965648220.50756548 1 1 0.96564822 3.995390993 0.998847748

It is easily seen in Table 20 that on lower levels some of the column 2return is sacrificed to increase the column 3 hit rate to allow morefrequent play of the lucrative upper levels as seen in column 6.

Finally, when only two or three stages are bet, the analysis must bedone again from the beginning, starting with the top stage and workingdown. The results for two or three stages are not inferable from theTable 20 data, but need to be developed independently.

It should be clear that a single stage game (i.e., a bet on only thefirst level) is no different than the standard 9-6 Jacks or Better game.

This third embodiment of a multi-stage draw poker gaming machine isoperationally summarized in the flow charts of FIGS. 27A-27F. FIG. 27Agenerally describes the start-up of the Multi-Strike Five-Card DrawPoker game embodiment, which is initially quite similar to that of thefirst (slots) embodiment. First, an assessment of whether credit(s) arepresent is undertaken beginning at step 270. If none is present, then acheck is made as to whether the player has inserted the relevant coin,credit card, etc., for the necessary credit(s) at step 271. If so, thenat step 272 the credit(s) are registered and displayed at the “TotalCredits” meter 77 (e.g., FIG. 17). All available player buttons are thenactivated for initiation of play at 275.

At this stage, the player enters a set-up loop where the player maychoose to add more credits or proceed with play at step 276. If creditsare added, these are registered on the meter display 77 at step 277. Thecards displayed from a previous hand, along with any stage total(s) andsubtotal(s) reflected in the payout information window(s), and “TotalWon” meter 85 are all cleared for the new game (step 278). The programloops back to step 276.

The “Coins per Hand” button 67 can alternatively be engaged from step276, causing the coins-per-hand setting to be modified (as indicated atmeter 64, FIG. 17), as well as updating the value of the “Total Bet”window 68, as indicated at step 279. Once again, the program loops backto step 276 through steps 278 and 275.

Back at step 276, the player then can choose the “Select Number ofHands” button 66 to input this aspect of his or her wager. This likewisecauses the “Total Bet” to be so modified, as well as displaying thenumber of hands bet at meter 63, all as indicated at step 280. Graphicsare also updated at step 281 to highlight the hands which are now“active” (i.e., potentially playable). Steps 278 and 275 then follow inthe loop back to step 276.

Once the player has input the parameters of the wager, then the “DealDraw” button 70 is engaged. It should be noted that the foregoingselection sequence as to coins and hands to bet need not follow theorder indicated.

The player has the option of skipping all of the hands and coins perhand selections, through resort to the “Max Bet Deal” button 76. Asubroutine will then execute at step 285 to assess the total credits theplayer has provided, and then determine the maximum number of coins perhand and the maximum number of hands (per an embedded look-up table)which can be played for that credit quantity, up to a fixed maximum forthe game. The graphics are updated accordingly at steps 286 and 287 toshow the hands being bet, coins-per-hand and total bet (as at steps 279and 280). Steps 288 and 289 then follow, and are the same as steps 281and 278, respectively.

From either the actuation of the “Deal Draw” button 70 or the “Max BetDeal button 76, the selection buttons for player input are thendeactivated and the amount bet is subtracted at step 291, with theremaining credits updated on the “Total Credits” meter 77. The main gameplay sequence is then begun (step 292).

The program randomly “shuffles” the deck to establish a playing orderfor the fifty-two regular playing cards (used in this version) at step293 (FIG. 27B). A determination is made as to whether the secondstage/level/hand is “active” (bet upon) at step 295. If it is not, theprogram proceeds to step 300 described below. If it is, then asubroutine is engaged for a “Free Ride” card (this version includingthis added feature). Beginning at step 296, a random selection process(discussed above) determines whether the “Free Ride” is available ornot. If it is, then the “Free Ride” card is caused to be registered inone of the first five positions representing the order of the cards inthe shuffled deck for the cards of the first hand (step 297), and the“Free Ride” feature will be available (as described hereafter). If it isnot, then no “Free Ride” card is displayed, and the “Free Ride” featureis not available.

From either step 296 or 297, the program then “deals” (step 300) thecards for the hand, displaying the cards graphically in the five spacesallotted in the first hand 71. A check is made in the course of theforegoing deal to determine if one of the dealt cards is a “Free Ride”card at step 301. If it is (i.e., the “Free Ride” feature is available),then the “Free Ride” card is caused to be displayed in the spacecorresponding to its placement in the order, as indicated at step 302.Whereupon there is an audio cue also provided, and much rejoicing isheard throughout the land (step 303). After a suitable interval, the“Free Ride” card is caused to be replaced by the next regular playingcard in the deck order (step 304), and a “Free Ride” icon is displayednext to the level (as seen at 91 in FIG. 25).

From step 304, or step 301 if no “Free Ride” is detected, the programthen performs an evaluation of the dealt hand (step 308) to determine ifa winning hand is presented, using the paytable hierarchy discussed withregard to FIG. 18, or more simply, is a pair of “Jacks or Better”presented (step 309)? If a winning hand is presented, then from step 309a message is graphically displayed indicating the hand “rank” along withan audio sound acknowledging to the player that a winner is already inhand (with or without rejoicing, as desired, rejoicing being playerdependent), as set forth in step 310. From either step 309 or 310, theprogram then advances to step 315.

Step 315 provides multiple options to the player at this juncture. Theplayer may choose to add more credits, for example, which if electedresults in an update to the “Total Credits” meter 77 at step 314, thenlooping back to step 315.

The player can also choose which cards to hold/discard at this point. Acard that is to be held is selected (step 316) and then tagged as “held”(step 317) (e.g., see FIG. 19 and related discussion). Cards previouslyselected for being held can likewise be de-selected (step 318). Fromeither step 317 or 318, the process loops back to step 315.

When the player has exercised whatever of the foregoing options aredesired, if any, from step 315, the “Deal/Draw” button 70 is againactuated. This results in the removal from the graphic display of anycard not designated as “held” (step 320). Each card removed is replacedwith the next card in the deck order, as indicated at step 321. Are-evaluation of the hand now presented takes place at steps 322 and325, similar to that of steps 308 and 309. If a winning hand ispresented (again with reference to the paytable of FIG. 18), the type ofwinner is identified (e.g., “Three Of A Kind,”) graphically for theplayer in the payout information window 84, along with the number ofcoins/credits won as a sub-total, all as indicated in step 326. Thatsub-total is increased by the stage multiplier (which in the case of thefirst level, is 1×) and displayed as a “total” for the first hand, atstep 327. From here, the first hand total is added to the “Total Won”meter amount at 85 (e.g., FIG. 20) (step 328).

If a winning hand is not presented at step 325, then a check is made asto whether the “Free Ride” icon is registered for the level at step 329.If it is, a message is displayed in payout information window 84 thatthe “Free Ride” feature is being employed to advance to the nextstage/level/hand (step 330). If the “Free Ride” is not registered, thenthe game is over, and progresses to a “Game Over” sequence 331.

Out of steps 328 or 330, the program determines if the secondstage/level/hand is “active,” i.e., bet upon (step 332). If it is not,the player is sent to the “Game Over” sequence (step 331). If it isactive, however, then it is on to the next level.

Referring to FIG. 27C, play and operation continue substantially similarto that described with respect to that of the first level. A “new” deckis “shuffled,” (step 333). As in the first level, a determination isthen made as to whether the third stage/level/hand is “active” (betupon) at step 335. Steps 335 through 337, 340 through 344 and 348through 350 are the same as their respective counterpart steps (295 etseq.) discussed with regard to the play of the first hand, albeit now inview of second level play.

From step 349 or step 350, a “draw” sequence is again executed asdescribed with respect to the first hand, beginning at step 355. Thisincludes the option of adding more credits (update of credit meter atstep 354), and the selection of cards to be “held” via steps 356 through358 (corresponding to steps 316 through 318, respectively, describedabove). Once card selection is completed at step 355, previouslydescribed steps 320 through 322, and 325 through 332 are repeated, butfor this second stage/level/hand, through respective steps 360 through362, and 365 through 372. At this point, either the game is over, andthe player is routed to the “Game Over” sequence (step 371), or theplayer advances to another hand that has been bet upon, and playadvances to the third stage/level/hand out of step 372, shown in FIG.27D.

Referring now to FIG. 27D (and, e.g., FIG. 21), play continues for thethird hand in the same manner as that described for the first and secondhands, albeit now in view of third level play. Accordingly, and for easeof description, steps described as to the first level are related totheir corresponding steps in the third level by grouping the respectivesteps as follows: 293/373, 295-297/375-377, 300-304/380-384,308-310/388-390, 314-318/394-398, 320-322/400-402, 325-332/405-412. Atthis point, either the game is over, and the player is routed to the“Game Over” sequence (step 411), or the player advances to another handthat has been bet upon, and play advances to the fourth stage/level/handout of step 412, shown in FIG. 27E.

Play of the fourth hand is similar to that described above, except thatno “Free Ride” is available (this being the last hand in this particularembodiment of the game). Accordingly (and using the same convention forgrouping like steps of the first and fourth levels for ease ofdescription), cards are “shuffled” at step 413/293, dealt at step420/300, and the hand is evaluated at step 428/308. If a winning hand ispresent (step 429/309), then a message is displayed at step 430/310.

Beginning with step 435, a “draw” sequence is again executed asdescribed with respect to the first hand. In this fourth level, stepsdescribed for the first level draw sequence correspond to their fourthlevel counterparts as follows: 314-318/434-438, 320-322/440-442, and325-328/445-448. Since there is no fifth level, the game proceeds to the“Game Over” sequence out of step 448 or step 445 at step 451.

The “Game Over” sequence is set forth in FIG. 27F. A “GAME OVER” messageis displayed by the graphics (step 452). The “Total Won” amount (meter85 in FIG. 20) is checked, and if greater than zero (step 453), thecredit(s) amassed as represented on the meter 85 are added to the “TotalCredits” meter 87 at step 454. The player, and the game, are bothreturned to the game start up sequence out of step 453 (if nothing won)or step 454.

Bunco

Bunco, sometimes called Bunko, Bonko or Bonco, is a dice game that datesback to the mid 1800's in the United States. While there are manyvariations that are currently played, what follows is what appear to bevery popular rules of the game.

Bunco is typically played in groups of eight to twenty players, usuallywomen and occasionally couples as a social event. A group typicallymeets once a month, and plays at multiple tables of four players.Players seated across from each other are partners although it istypical to change partners for each game played. Each table has threedice that are passed around from player to player.

The game is played in “rounds”. The first round starts with all tablesrolling for a “point” of one. The dice move clockwise to each person atthe table who gets to roll the dice. A team scores one point for eachdie that matches the current point (one in this case). Each time one ormore dice match the current point, the player's team scores and theplayer continues to roll. If the player gets all three dice to match ona number other than the current point then that team scores five pointsand the player continues to roll. If the player gets all three dice tomatch the current point they yell out “Bunco” and the team is awardedtwenty-one points.

Once a player rolls the dice showing no points, the turn ends. Eachround continues with the dice going from player to player around thetable. The game ends when a player at the first or head table reachestwenty-one points, which is usually indicated by ringing a hand-bell tosignal all the tables that the round is over. At this point the playerschange partners and rotate through the tables based on the winners andlosers, and the next game would play with a “point” of two.

This fourth embodiment of the current invention consists of a dice gamethat is loosely based on an individual player's turn during a round ofBunco. While this game may be played in a casino with live dealers (asis done with the casino game of Craps) or on a gaming machine thatpropels real physical dice, the preferred embodiment is on a videogaming machine.

Unlike the version of Bunco described above, in this fourth embodimentthere may be up to three points which the player is trying to roll.Instead of being a single number, any number that has been rolled onevery stage of the current game is an active point. On the first roll,each number that appears on a die becomes a point, for a possible totalof three points if all three dice are different (that is, all sixpossible numbers are points for the first roll). On the second roll, theplayer must roll one or more points matching the first roll to keep thegame going. Any numbers that were rolled on both the first and secondrolls remain points for the third roll. The player continues to rolluntil no dice match a number found in all previous rolls, or until thehighest stage upon which a bet has been placed is rolled.

FIG. 28 shows a display of this fourth embodiment. A maximum of sevenstages or rolls of the dice per game is provided. The game may allowmore or fewer stages without departing from the invention. Each stage(level) of the game represents a roll of the dice as described above.The player may place a bet on from one to seven stages or lines. Theplayer may bet from one to five coins per stage in this version. Ofcourse, it is anticipated that different numbers of coins per stagecould be allowed. Also, the player could be allowed to place bets ondifferent stages at random, rather than from the bottom up. For thatmatter, the player could be allowed to make different size wagers ondifferent stages at will, without departing from the invention.

Referring to FIG. 28, the “Select Lines” button 100 is pressed to selectfrom one to seven stages to bet on. The “Coins per Line” button 101 ispressed to indicate the number of coins to bet on each line. The playerthen presses the “Roll Dice” button 102 to roll the dice for the firststage.

FIG. 29 shows a game in progress after the first roll. This roll of3-4-6 is placed in the first stage area 105 next to the applicable lineof the paytable 106 for that stage (0,0,0,32). For each stage there arefour paytable values. These values are for rolling one, two or threepoints or for rolling “Bunco,” which is achieved when all three dicematch one number which is an active point. Only the highest value ispaid at each stage, so a “Bunco” does not also pay for three pointsmatched. For the first roll (with all six numbers active) anycombination of three matching dice is a “Bunco.” Scoring a “Bunco” isthe only way to win the first level bet, although in this game theplayer automatically advances to the second stage. It is envisioned thatother embodiments could set the active points in advance of the firstroll which would then require a match on the first roll to continue. Afirst stage “Bunco” awards thirty-two coins. The machine highlights theappropriate paytable value in the “3 points matched” column for thisroll and shows the remaining points under the first stage line (107).

The player presses the “Roll Dice” button 102 for the second stage, anda possible result is shown in FIG. 30. The roll of 1-4-6 matches two ofthe three points that were established in the first roll. Thus, thepoints “4” and “6” remain “alive,” i.e., in play (107). The point of “3”from the first roll is no longer alive because it does not appear in thesecond roll. The three dice are placed on the second stage line 108 nextto the applicable paytable 106 values for that stage. The gamehighlights the “2 points matched” value in the paytable indicating thatone coin is awarded for matching two points on the second stage. The“Total So Far” meter 110 is updated to show the total of one coin won atthis point (zero coins on the first stage and one coin on the secondstage). The window 107 under the first stage now shows that only the “4”and the “6” remain as active points.

The player presses the “Roll Dice” button 102 for the third stage and apossible result is shown in FIG. 31. The roll of 1-1-6 matches one ofthe two points that were alive after the second roll. Thus, only thepoint “6” remains alive (107). The point of “4” from the first two rollsis no longer alive because it does not appear in the third roll. Thethree dice are placed on the third stage line 112 next to the paytablevalues for that stage. The game highlights the “1 point matched” valuein the paytable indicating that two coins are awarded for matching onepoint on the third stage. The “Total So Far” meter 110 is updated toshow the total of three coins won at this point (zero coins on the firststage, one coin on the second stage and two coins on the third stage).The window 107 under the first stage now shows that only the “6” remainsas an active point.

The player presses the “Roll Dice” button 102 for the fourth stage and apossible result is shown in FIG. 32. The roll of 1-4-5 does not matchthe point of “6,” which was the only point left alive. While “4” was anactive point after the first two rolls, the absence of a “4” on thethird roll took it out of play as a point, and thus was of no value inthe fourth roll. As a result of matching no points the game is over. The“Total So Far” meter 110 value of three coins is copied to the “Paid”window 114, and this is added to the credits counter 115 taking it froman arbitrary“865” to “868” credits.

It should be noted that in the example shown, the bets for levels abovethe fourth level were lost without those levels being played. As isintuitive and will be shown in the following analysis, the higher thelevel, the less often it will be played. This is offset by offering theplayer very large awards for very modest events on these higher levelswhen they are played.

It should also be noted that while the slot machine and pokerembodiments previously discussed have stages that are independent gamesthat allow advancing to the next stage upon winning, this fourth Buncoembodiment is an ongoing game with stages that, as a result of thenature of the game, also involve multi-stage betting working with anevolving game. This game is not limited to advancing to the next stageonly with a win, since the game will always play the second stage if twoor more stages have been bet upon, even though, except for a first stage“Bunco”, the player will not win on the first stage.

FIG. 33 shows another Bunco game at its conclusion. The first roll of1-5-5 established only two points as a result of the duplicate 5's. Thesecond roll of 1-3-3 kept only the point of “1” alive. The third roll of1-1-1 is “Bunco” scoring fourteen coins. The fourth roll of 3-4-6 doesnot match the point of “1”, and thus ends the game. A total of fifteencoins were won on this game (one for matching one point on the secondstage and fourteen for “Bunco” on the third stage).

Looking at FIG. 33, the “Max Bet/Roll Dice” button 116 is also seen.This button 116 establishes the maximum bet, which in this embodiment isthirty-five coins, (seven stages times five coins per stage) and thenrolls the dice for the first stage. Pressing this button 116 is the sameas pressing the “Select Lines” button 100 until seven lines areselected, and then pressing the “Coins per Line” button 101 until fivecoins per line are selected, and then finally pressing the “Roll Dice”button 102 to roll the dice for the first stage.

Shown in the upper right section of FIG. 33 are the bonuses for gamesthat achieve two “Buncos” and three “Buncos”: “75” coins and “2500”coins respectively. These bonuses add excitement to the game, as well asthe opportunity to win a more sizable award than is available from theseven stages of the game.

The foregoing Bunco gaming machine is operationally summarized in theflow charts of FIGS. 34A through 34D. FIG. 34A generally describes thestart-up of the Multi-Strike BUNCO game embodiment, which is initiallyquite similar to that of the first (slots) embodiment. First, anassessment of whether credit(s) are present is undertaken beginning atstep 460. If none is present, then a check is made as to whether theplayer has inserted the relevant coin, credit card, etc., for thenecessary credit(s) at step 461. If so, then at step 462 the credit(s)are registered and displayed at the “Credits” meter 115 (e.g., FIG. 28).All available player buttons are then activated for initiation of playat 465.

At this stage, the player enters a set-up loop where the player maychoose to add more credits or proceed with play at step 466. If creditsare added, these are registered on the meter display (115) at step 468.The program loops back to step 466.

The “Coins per Line” button 101 can alternatively be engaged from step466, causing the coins-per-line setting to be modified (as indicated atmeter 103, FIG. 28), as well as updating the value of the “Total Bet”window 104, and the paytable information window 106, all as indicated atstep 469. Once again, the program loops back to step 466.

Back at step 466, the player can choose the “Select Lines” button 100 toinput this aspect of his or her wager. Graphics are updated at step 470to highlight the lines which are now “active” (i.e., potentiallyplayable). This likewise causes the lines bet meter 111 and “Total Bet”104 to be so modified, all as indicated at step 472. The program onceagain loops back to step 466.

Once the player has input the parameters of the wager, then the “RollDice” button 102 is engaged. It should be noted that the foregoingselection sequence as to coins and lines to bet need not follow theorder indicated.

The player has the option of skipping all of the lines andcoins-per-line selections, through resort to the “Max Bet Roll Dice”button 116 (FIG. 33). A subroutine will then execute at step 475 toassess the total credits the player has provided, and determine themaximum number of coins per line and the maximum number of lines (per anembedded look-up table) which can be played for that credit quantity, upto a fixed maximum for the game. The graphics are updated accordingly atsteps 476 and 477 to show the lines being bet, coins-per-lines and totalbet (as at steps 469, 470 and 472). Either out of step 477 or afteractuation of the “Roll Dice” button 102, the player selection buttonsare deactivated (step 478), the sum of the wager is subtracted from the“Credits” meter 115 and the new amount is displayed. The game thenprogresses to a main play sequence (step 479).

The dice are rolled at step 480, as shown in FIG. 34B. The programassesses whether this is the first roll of the game (step 482). If it isthe first roll, then “Match these POINTS” window 107 (e.g., see FIG. 29)is activated at step 483, and a determination is made as to how manydifferent numbers are presented by the rolled dice (step 484). Thedifferent “Points” are then displayed in the window 107, depending onwhether there are one, two or three different numbers (steps 485 athrough 485 c). The graphics of the program generates copies of the dicerolled, with a color hue to indicate a “Point Made” at step 488, and thedice are displayed in the current stage/level/roll (step 489), whichhere is the first level 105.

If this is not the first roll of the game (step 482), then copies of thedice just rolled are generated at step 490. The program executes acomparison of the numbers (dice) in the window 107 (which are the Pointsto match), with the dice just rolled at step 491. If there is a match,the graphics of the program colors a copy (or copies) of the matchingdie rolled with a hue to indicate a “Point Made” at step 492. For eachmatch not made, the die (dice) is colored with a hue to indicate that nomatch/Point was made (step 493), and the dice are displayed as so huedin the current stage/level/roll (step 489).

From step 489, another comparison is then made at step 495 between thecurrent roll and the Point(s) to be matched/made. Each Point in thewindow 107 is assessed as to a match on a die (number) of the currentroll at step 496. If at step 496 there is no match for a Point, it isremoved from the game and the graphics of window 107 are updatedaccordingly, at step 498. The program then assesses whether there is anyPoint remaining (step 497), and the game proceeds to a “Bunco”determination if the answer to the foregoing is positive. If there areno Points remaining (window 107), the player is passed to a “Game Over”sequence at step 500.

The “Bunco” assessment is set forth in FIG. 34C. The program firstassesses whether a “Bunco” has been rolled at step 501. If theevaluation is positive, then the graphics highlight the “BUNCO” pay(see, e.g., 113 in FIG. 33) for the current level (step 502). That“BUNCO” pay amount is added to the “Total So Far” meter 110 at step 503.

The program then determines whether two “Bunco's” had previously beenrolled in the same game at step 506. If “yes,” then the “Triple BUNCOBONUS” is highlighted on the screen (step 507), and the predeterminedamount for that bonus is added to the “Total So Far” meter 110 at step508.

If two “Bunco's” have not been registered at step 506, the program makesa determination as to whether one “Bunco” had previously been scored atstep 510. If “yes,” then the “Double BUNCO BONUS” is highlighted on thescreen (step 512), and the predetermined amount for that bonus is addedto the “Total So Far” meter 110 at step 513.

Back at step 501, if a “Bunco” has not been rolled, then a count is madeof the number of rolled dice that match any of the remaining Points inthe window 107 (step 515). That count is used to highlight theappropriate pay for that level for that number of points in the paytableinformation window as indicated at step 516. That amount is added to themeter 110 at step 517.

Out of either step 508, 513 or 517, the player then advances to step520, which is a program assessment as to whether all lines that havebeen bet on have been played. If all have been played, then the game isover and the “Game Over” sequence is engaged out of step 521.

If all possible lines have not been played, then the player is given theoption of adding more credits and/or continuing through actuation of the“Roll Dice” button 102 at step 525. If the choice is to add credits,then the “Credits” meter is so updated at step 526, and the player islooped back to step 525. If the choice is to roll, then another round isstarted (step 527) upon actuation of the button 102, whereupon thesequence of events beginning at step 480 recommences.

Once all lines have been played or there are no Points left in thewindow 107 (i.e., no match at a level), then the “Game Over” sequence ofFIG. 34D is engaged. A “GAME OVER” message is displayed at step 530, anda determination is made as to whether the “Total So Far” meter 110 showsany credits (i.e., any winnings for the game) at step 531. Any winningsas shown in meter 110 are then added to the total “Credits” meter 115(step 532), and the player and the program are returned to the gamestart sequence at step 460.

Analysis of Certain Architecture of the Bunco Embodiment

The mathematical payout percentage of this fourth embodiment isdetermined by breaking down the different possible combinations for eachof the seven stages. This will be done for one coin per line only, as itis well known by those skilled in the art how to expand this result formultiple coins per line, as well as the inclusion of bonus values, ifdesired. The first stage is fairly easy to analyze. There are threepossible types of outcome of the first roll: “Bunco” (equivalent to onepoint established), two points established or three points established.There are two hundred and sixteen possible combinations of three dicecomputed by multiplying the possible combinations of each die:6×6×6=216. The number of occurrences of “Bunco” or three dice that matchare six. This is computed as 6×1×1 because the first die can take any ofthe six numbers, then the second die must match that number and thethird die must also match that number. Three points are established whenall three of the dice have a different number showing, and is computedby 6×5×4=120 because the first die can take on any value while thesecond die can take on any of the five remaining values that don't matchthe first die, and the third die can then take on any of the remainingvalues that don't match the first two dice.

This leaves ninety occurrences of a combination that results in twopoints (216−6−120=90). The ninety occurrences of two points can also becomputed directly as follows: There are three forms that a rollresulting in two points may take: XYX, XXY or YXX. The combinations forthese are as follows:

-   -   XYX=6×5×1=30 First can be any, second must not match first,        third must match first.    -   XXY=6×1×5=30 First can be any, second must match first, third        must not match first.    -   YXX=5×6×1=30 First can be any but X, second can be any, third        must match second.

Table 21 organizes the data described above. The first column indicatesthe number of points established by the first roll. The second columnshows the value paid for that result. The third column shows the“Occurrences” of that result which was determined above. The fourthcolumn is the probability of that result, which is the occurrence countdivided by 216, the number of possible outcomes. The fifth column is theExpected Value component from each pay, which is the product of thepaytable value times the probability of receiving that value. The sum ofall EV components is the expected return of the stage, which is 88.89%.If only stage one was played, then the expected return to the playerwould be 88.89%. The payout percentage may be modified by making achange to the second column “Pay” value, which would also change in thepaytable. For example, changing the pay for “Bunco” (one pointestablished) from “32” to “33” would result in a 91.67% expected return.Unlike the slot machine example, the “Occurrence” data is locked intothe rules of the game, and any change to the payout will be apparent tothe player. It must be done by modifying the paytable as describedabove, or by changing the rules of the game.

TABLE 21 Number of Points Pay Occurrences Probability EV 1 32 60.027777778 0.888889 2 0 90 0.416666667 0 3 0 120 0.555555556 0 216 10.888889

The second stage of the game has three separate analyses based on thenumber of points established in the first stage of the game. The“Occurrences” for each row in Table 22 (the fourth column) arecalculated in the same manner as shown for the first stage and will notbe elaborated on further. The first column of Table 22 states the numberof points alive at the start of the second stage. This table has threeseparate analyses based on whether one, two or three points were aliveat the start of the second stage.

The second column shows the combination being enumerated. The threepossible points are called “A”, “B” and “C”. “x” indicates a die thatmatches no point. The “Comb. Column” shows the makeup of the dice forthat line of the table. For example, AAA is three dice matching point“A”. The BBA is two dice matching point “B” and one die matching point“A”, and this can occur in any order. The third column indicates theamount paid for the specified combination. This is based on the secondstage paytable line of 1,1,2,6 (e.g., FIG. 30) awarding one coin formatching one or two points, two coins for matching three points in anon-“Bunco” combination and six coins for all three dice matching thesame point (“Bunco”). The fourth column indicates the number ofoccurrences of the specified combination out of the possible two hundredand sixteen combinations. The fifth column is the probability of thatoccurrence and is the quotient of the occurrences and the two hundredand sixteen possible combinations. The sixth column is called“Probability of Start Condition”. This is the probability of startingthe second stage with the number of points shown in the first column.This number is taken directly from Table 21.

The seventh column is the probability of the specified “Result”occurring, which is the product of the fifth and sixth columns. Thisresult is due to the need for the probability of the sixth column tostart the stage with the number of points specified in the first column,as well as the need for the probability of the combination, which isgiven in the fifth column.

The eighth column is the expected value contribution from thiscombination which is computed as the product of the “Pay” value timesthe seventh column “Probability of this Result”. The sum of all valuesin the eighth column provides the expected return which is 92.28%.

The ninth column is the number of points still alive after the roll.This is represented by the number of unique capitalized letters in thesecond column combination.

The last four columns are used to determine the probability of thenumber of points alive at the end of the stage. The seventh column“Probability of This Result” value is copied to the column thatcorresponds to the ninth column “Points Alive” number. For example, forAAA there is one point alive which results in the 0.00013 value to becopied from the seventh column to the eleventh column, which is thecolumn that calculates the “Probability that Points Left=1”.

The bolded numbers at the bottom of the last four columns of Table 22tally the probability of ending the second round with the number ofPoints specified at the head of the column. For example, of the gamesthat play a second stage (which is all games in this embodiment), 24.31%will finish the second stage with two points active.

TABLE 22 Points Alive Points Prob. Prob. Prob. Prob. at ProbabilityProb. Of Alive That That That That Round Probability of of Start ThisAfter Points Points Points Points Start Comb. Pay Occur. OccurrenceCondition Result EV Roll Left = 0 Left = 1 Left = 2 Left = 3 1 AAA 6 10.00462963 0.02777778 0.000129 0.000772 1 0.00013 1 AAx 1 15 0.069444440.02777778 0.001929 0.001929 1 0.00193 1 Axx 1 75 0.34722222 0.027777780.009645 0.009645 1 0.00965 1 xxx 0 125 0.5787037 0.02777778 0.016075 00 0.01608 216 1 2 AAA 6 1 0.00462963 0.41666667 0.001929 0.011574 10.00193 2 BBB 6 1 0.00462963 0.41666667 0.001929 0.011574 1 0.00193 2AAB 2 3 0.01388889 0.41666667 0.005787 0.011574 2 0.00579 2 BBA 2 30.01388889 0.41666667 0.005787 0.011574 2 0.00579 2 AAx 1 12 0.055555560.41666667 0.023148 0.023148 1 0.02315 2 BBx 1 12 0.05555556 0.416666670.023148 0.023148 1 0.02315 2 ABx 1 24 0.11111111 0.41666667 0.0462960.046296 2 0.0463 2 Axx 1 48 0.22222222 0.41666667 0.092593 0.092593 10.09259 2 Bxx 1 48 0.22222222 0.41666667 0.092593 0.092593 1 0.09259 2xxx 0 64 0.2962963 0.41666667 0.123457 0 0 0.12346 216 1 3 AAA 6 10.00462963 0.55555556 0.002572 0.015432 1 0.00257 3 BBB 6 1 0.004629630.55555556 0.002572 0.015432 1 0.00257 3 CCC 6 1 0.00462963 0.555555560.002572 0.015432 1 0.00257 3 AAB 2 3 0.01388889 0.55555556 0.0077160.015432 2 0.00772 3 AAC 2 3 0.01388889 0.55555556 0.007716 0.015432 20.00772 3 BBA 2 3 0.01388889 0.55555556 0.007716 0.015432 2 0.00772 3BBC 2 3 0.01388889 0.55555556 0.007716 0.015432 2 0.00772 3 CCA 2 30.01388889 0.55555556 0.007716 0.015432 2 0.00772 3 CCB 2 3 0.013888890.55555556 0.007716 0.015432 2 0.00772 3 ABC 2 6 0.02777778 0.555555560.015432 0.030864 3 0.01543 3 ABx 1 18 0.08333333 0.55555556 0.0462960.046296 2 0.0463 3 ACx 1 18 0.08333333 0.55555556 0.046296 0.046296 20.0463 3 BCx 1 18 0.08333333 0.55555556 0.046296 0.046296 2 0.0463 3 AAx1 9 0.04166667 0.55555556 0.023148 0.023148 1 0.02315 3 BBx 1 90.04166667 0.55555556 0.023148 0.023148 1 0.02315 3 CCx 1 9 0.041666670.55555556 0.023148 0.023148 1 0.02315 3 Axx 1 27 0.125 0.555555560.069444 0.069444 1 0.06944 3 Bxx 1 27 0.125 0.55555556 0.0694440.069444 1 0.06944 3 Cxx 1 27 0.125 0.55555556 0.069444 0.069444 10.06944 3 xxx 0 27 0.125 0.55555556 0.069444 0 0 0.06944 216 1 EV ofsecond Stage: 0.92284 Prob. Of Start Cond. For Next Stage 0.208980.53254 0.24306 0.01543 Total of 4 probability values above 1

Table 23 provides a similar analysis for the third stage of the game.The first two columns are the same. The third column has been modifiedto reflect the 2-2-5-14 (e.g., FIG. 31) paytable values for the thirdstage. The fourth column is the same as Table 22.

The fifth column uses the “Probability of Start Condition” for thespecified number of points taken from the bottom of Table 22. Thosenumbers at the bottom of Table 22 show the probability of ending thesecond stage with zero, one, two or three points. The values in the restof the columns are calculated in the same manner as was described forTable 22.

Looking at the sum of the “EV” column, it is clear that the expectedreturn for the third stage of the game is 90.24%. The right four columnsare used to compute the probability of zero, one, two or three pointsremain alive after the third stage. Note that the sum of theseprobability values does not total 1.0, but rather 0.79102. Theadditional component is the 0.20898 found at the bottom of Table 22under “Probability that Points Left=0”. This represents games that endedafter two stages and thus are not reflected in the stage three endingbreakdown. In the same manner, the 0.3821 probability of ending the gamein the third stage will not be included in the stage four endingbreakdown.

The analysis for stages four through seven is done in a manner identicalto stage three. The comparable tables for these stages are therefore notshown.

TABLE 23 Points Alive Points Prob. Prob. Prob. Prob. at ProbabilityProb. Of Alive That That That That Round Probability of of Start ThisAfter Points Points Points Points Start Comb. Pay Occur. OccurrenceCondition Result EV Roll Left = 0 Left = 1 Left = 2 Left = 3 1 AAA 14 10.00462963 0.532536 0.0024654 0.0345162 1 0.0025 1 AAx 2 15 0.069444440.532536 0.0369817 0.0739633 1 0.037 1 Axx 2 75 0.34722222 0.5325360.1849083 0.3698167 1 0.1849 1 xxx 0 125 0.5787037 0.532536 0.3081806 00 0.3082 216 1 2 AAA 14 1 0.00462963 0.2430556 0.0011253 0.0157536 10.0011 2 BBB 14 1 0.00462963 0.2430556 0.0011253 0.0157536 1 0.0011 2AAB 5 3 0.01388889 0.2430556 0.0033758 0.0168789 2 0.0034 2 BBA 5 30.01388889 0.2430556 0.0033758 0.0168789 2 0.0034 2 AAx 2 12 0.055555560.2430556 0.0135031 0.0270062 1 0.0135 2 BBx 2 12 0.05555556 0.24305560.0135031 0.0270062 1 0.0135 2 ABx 2 24 0.11111111 0.2430556 0.02700620.0540123 2 0.027 2 Axx 2 48 0.22222222 0.2430556 0.0540123 0.1080247 10.054 2 Bxx 2 48 0.22222222 0.2430556 0.0540123 0.1080247 1 0.054 2 xxx0 64 0.2962963 0.2430556 0.0720165 0 0 0.072 216 1 3 AAA 14 1 0.004629630.0154321 7.144E−05 0.0010002 1 7E−05 3 BBB 14 1 0.00462963 0.01543217.144E−05 0.0010002 1 7E−05 3 CCC 14 1 0.00462963 0.0154321 7.144E−050.0010002 1 7E−05 3 AAB 5 3 0.01388889 0.0154321 0.0002143 0.0010717 20.0002 3 AAC 5 3 0.01388889 0.0154321 0.0002143 0.0010717 2 0.0002 3 BBA5 3 0.01388889 0.0154321 0.0002143 0.0010717 2 0.0002 3 BBC 5 30.01388889 0.0154321 0.0002143 0.0010717 2 0.0002 3 CCA 5 3 0.013888890.0154321 0.0002143 0.0010717 2 0.0002 3 CCB 5 3 0.01388889 0.01543210.0002143 0.0010717 2 0.0002 3 ABC 5 6 0.02777778 0.0154321 0.00042870.0021433 3 0.00043 3 ABx 2 18 0.08333333 0.0154321 0.001286 0.002572 20.0013 3 ACx 2 18 0.08333333 0.0154321 0.001286 0.002572 2 0.0013 3 BCx2 18 0.08333333 0.0154321 0.001286 0.002572 2 0.0013 3 AAx 2 90.04166667 0.0154321 0.000643 0.001286 1 0.0006 3 BBx 2 9 0.041666670.0154321 0.000643 0.001286 1 0.0006 3 CCx 2 9 0.04166667 0.01543210.000643 0.001286 1 0.0006 3 Axx 2 27 0.125 0.0154321 0.001929 0.0038581 0.0019 3 Bxx 2 27 0.125 0.0154321 0.001929 0.003858 1 0.0019 3 Cxx 227 0.125 0.0154321 0.001929 0.003858 1 0.0019 3 xxx 0 27 0.125 0.01543210.001929 0 0 0.0019 216 1 EV of third Stage: 0.9023574 Prob. Of StartCond. For Next Stage 0.3821 0.3696 0.0389 0.00043 Total of 4 probabilityvalues above 0.79102

The analysis provided thus far does not include the bonuses for two“Buncos” and three “Buncos” occurring in the same game. The probabilityof getting a second or third “Bunco” in a game must be analyzed on astage by stage basis, with the expected value of such awards added tothe EV of the stage in which the bonus occurs.

A double “Bunco” award is given on a particular stage when the second“Bunco” in a game is achieved in that stage. It is not possible to get adouble “Bunco” in the first stage. In the second stage, the only way toachieve a double “Bunco” bonus is to roll a “Bunco” on each of the firsttwo stages. On the third stage, one could get “Bunco” on the first andthird stage, or the second and third stage (the first and second stageis the case noted above of getting a double “Bunco” on the secondstage). The shorthand ×BB is used to indicate no “Bunco” on the firststage followed by “Bunco” on the second and third stages, whilesimilarly B×B indicates “Bunco” on the first and third stages with no“Bunco” on the second stage.

Table 24 shows the combinations that will result in a double “Bunco” onthe seventh stage. Note that all combinations must have the second“Bunco” occur as the seventh stage because if the second “Bunco”occurred earlier then it would be attributed to the earlier stage.

TABLE 24 BxxxxxB xBxxxxB xxBxxxB xxxBxxB xxxxBxB xxxxxBB

Working through the cases in Table 24, it is found that as a result ofsymmetry, the probability of each of these components to a seventh leveldouble “Bunco” is identical. Likewise, there are five ways of identicalprobability to achieve a sixth level double “Bunco” bonus and the twoways mentioned above to achieve a third level double “Bunco” bonus haveidentical probability.

In order to compute the probability of the required components, there isa need to use three values that were computed earlier. In Table 21, theprobability of a “Bunco” on the first roll is shown to be 0.027777778.The “x” components in the first line of Table 24 is the probability ofstaying alive in a game that has established one point, by rollinganything but a “Bunco”. This is found by taking the second and thirdlines of Table 22 (AAx and Axx) and adding the probability of thoserolls (fourth column), which results in a total of 0.416666667. Finally,there is the probability of rolling a “Bunco” while one point is alive.This is shown in the first line of Table 22 (AAA) as 0.00462963. Usingthese values, one may construct the double “Bunco” probability table ofTable 25.

The first column of Table 25 shows the game “Stage” for which theprobability of double “Bunco” is being computed. The second column isthe “Number of Forms” a double “Bunco” may take on that stage (such asthe six forms shown for the seventh stage in Table 24). The third columnshows the “Sample Form” being computed for the stage. The fourth throughtenth columns are the probability components matching the respectiveletters in the third column forms. The eleventh column is the“Probability” of getting a double “Bunco” on that level which is theproduct of the second column form count and all probability components(“Comp.” 1 through 7).

TABLE 25 Number Double of Sample Bunco Stage Forms Form Comp. 1 Comp. 2Comp. 3 Comp. 4 Comp. 5 Comp. 6 Comp. 7 Probability 1 0 0 2 1 BB0.027778 0.00463 0.000128601 3 2 BxB 0.027778 0.416667 0.004630.000107167 4 3 BxxB 0.027778 0.416667 0.416667 0.00463 6.69796E−05 5 4BxxxB 0.027778 0.416667 0.416667 0.416667 0.00463 3.72109E−05 6 5 BxxxxB0.027778 0.416667 0.416667 0.416667 0.416667 0.00463 1.93807E−05 7 6BxxxxxB 0.027778 0.416667 0.416667 0.416667 0.416667 0.416667 0.004639.69033E−06

The analysis for the “Triple Bunco Bonus” is similar to the “DoubleBunco Bonus.” Table 26 shows all of the possible forms of a seventhlevel “Triple Bunco Bonus.”

TABLE 26 BBxxxxB BxBxxxB BxxBxxB BxxxBxB BxxxxBB xBBxxxB xBxBxxB xBxxBxBxBxxxBB xxBBxxB xxBxBxB xxBxxBB xxxBBxB xxxBxBB xxxxBBB

Using the same symmetry that was used for the double “Bunco”calculation, one arrives at Table 27.

TABLE 27 Number Triple of Sample Bunco Stage Forms Form Comp. 1 Comp. 2Comp. 3 Comp. 4 Comp. 5 Comp. 6 Comp. 7 Probability 1 0 0 2 0 0 3 1 BBB0.027778 0.00463 0.00463 5.95374E−07 4 3 BBxB 0.027778 0.00463 0.4166670.00463 7.44218E−07 5 6 BBxxB 0.027778 0.00463 0.416667 0.416667 0.004636.20181E−07 6 10 BBxxxB 0.027778 0.00463 0.416667 0.416667 0.4166670.00463 4.30682E−07 7 15 BBxxxxB 0.027778 0.00463 0.416667 0.4166670.416667 0.416667 0.00463 2.69176E−07

Table 28 shows the expected return from the double “Bunco” and triple“Bunco” awards. The first column shows the game “Stage”. The secondcolumn shows the “75” coin pay for the “Double Bunco Bonus”. The thirdcolumn shows the “Double Bunco Probability” computed in Table 25 foreach stage. The fourth column computes the expected return” (EV) fordouble “Buncos” on the given stage by multiplying the “Pay” (secondcolumn) times the “Probability” (third column). The fifth throughseventh columns compute the triple “Bunco” expected return in the samemanner as was used for “Double Bunco” in the second through fourthcolumns.

TABLE 28 Double Double Double Triple Triple Triple Bunco Bunco BuncoBunco Bunco Bunco Stage Pay Prob. EV Pay Prob. EV 1 75 0 0 2500 0 0 2 750.000129 0.009645 2500 0 0 3 75 0.000107 0.008038 2500 5.95E−07 0.0014884 75  6.7E−05 0.005023 2500 7.44E−07 0.001861 5 75 3.72E−05 0.0027912500  6.2E−07 0.00155 6 75 1.94E−05 0.001454 2500 4.31E−07 0.001077 7 759.69E−06 0.000727 2500 2.69E−07 0.000673

Finally, the overall EV of each stage and the overall EV of multi-stagegames is shown in Table 29. The first column indicates the “Stage”number. The second column shows the expected return for the base gamestage which was generated for the first three stages in Table 21, Table22, and Table 23. The third and fourth column show the “Double” and“Triple Bunco” bonus EV components generated in Table 28. The fifthcolumn is the total EV for the stage, which is created by adding the EVcomponents in the second, third and fourth columns. The sixth column isthe EV of an entire multi-stage game that bet on the number of stages inthe first column. This is the average of the fifth column in the currentrow and all rows above (i.e., the average EV of all stages in themulti-stage game). The expected return of the entire game when a playerplays all seven stages is 0.927423292 or 92.74%.

TABLE 29 Base Double Triple EV of Game Game Bunco Bunco Total EV Playingthis Stage EV EV EV For Stage many stages 1 0.888889 0 0 0.8888890.888888889 2 0.92284 0.009645 0 0.932485 0.910686728 3 0.9023570.008038 0.001488 0.911883 0.911085629 4 0.921469 0.005023 0.0018610.928353 0.915402545 5 0.953178 0.002791 0.00155 0.957519 0.923825811 60.937292 0.001454 0.001077 0.939822 0.92649184 7 0.931612 0.0007270.000673 0.933012 0.927423292

It will additionally be noted that the invention further contemplates atraining program for players of these games, particularly in the videogame versions. Such training programs are designed to teach players notonly the fundamentals of game play, but to optimize game playingstrategy, as with visual and aural cues for the player, replay options,and the like. Representative training programs are disclosed inapplicants' co-pending patent application Ser. No. 09/539,286, filedMar. 30, 2000, and that disclosure is hereby incorporated by reference.

Thus, while the invention has been disclosed and described with respectto certain embodiments, those of skill in the art will recognizemodifications, changes, other applications and the like which willnonetheless fall within the spirit and ambit of the invention, and thefollowing claims are intended to capture such variations.

1. A method carried out by a gaming machine, the method comprising:receiving a primary wager; receiving an additional wager; determining agame outcome; if the game outcome is a winning outcome, awarding aprimary payout based on the primary wager, and determining whether toaward an additional payout; and upon determining to award the additionalpayout, determining an additional-payout multiplier, and awarding theadditional payout based on the additional wager and theadditional-payout multiplier.